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U. S. MILITARY ACAOeivlV.
COURSE OF INSTRUCTION
IN
ORDNANCE AND GUNNERY
TEXT.
BY-
Captain HENRY METCALFE,
Ordnance Dep't, U. S. Army,
Instructor of Ordnance and G winery, U. S. Military Academy.
SKCOND KDITION.
^^ OP TEra"^^
UHiyERSITY]
*^^^ — 1891.
Copyright, 1891,
BY
Henry Metcalfe.
CONTENTS
CHAPTER
I.
CHAPTER
II.
CHAPTER
III.
CHAPTER
IV.
CHAPTER
V.
CHAPTER
VI.-
CHAPTER
VII.-
CHAPTER
VIII.
CHAPTER
IX.-
CHAPTER
X.
CHAPTER
XI.-
CHAPTER
XII.-
CHAPTER
XIII.-
CHAPTER
XIV.-
CHAPTER
XV.
CHAPTER
XVI.-
CHAPTER
XVII.-
CHAPTER
XVIIL-
CHAPTER
XIX.-
CHAPTER
XX.-
CHAPTER
XXI.-
CHAPTER
XXII.-
CHAPTER
XXIII.-
CHAPTER
XXIV.-
CHAPTER
XXV.-
CHAPTER
XXVI.-
CHAPTER
XXVII.-
CHAPTER :
XXVIII.-
CHAPTER
XXIX.-
CHAPTER
XXX.-
-Definitions. )
-Explosive Agents.
-Ingredients of Gunpowder. ,
-Manufacture of Gunpowder. J
-Interior Ballistics.
-Velocimeters.
-Pressure Gauges.
-Phenomena of Conversion.
-Noble and Abel's Experiments.
-Combustion of Gunpowder in the Air.
-Combustion of Gunpowder in the Gun.
-Sarrau's Formula for Interior Ballistics.
-History of Gunpowder.
-High Explosives. - /
-Metallurgy.
-Projectiles and Armor.
-Manufacture of Projectiles.
-Means of Communicating Fire.
-Gun Construction.
-Exterior Ballistics.
-Varieties of Cannon.
-Artillery Carriages, Principles.
-Various Artillery Carriages.
-Horse and Harness.
-Artillery Machines.
-Hand Arms. - {
-Small Arm Ammunition.
-Small Arms. '- 1
-Cannon Without Recoil.
-Accuracy of Fire.
PREFACE TO SECOND EDITION,
The great advances which have been recently made in our
knowledge of the properties of gunpowder have subjugated
the " Spirit of Artillery," as this agent has been termed, to a
seemingly docile servitude. These, with corresponding
improvements in Metallurgy, have led to such changes in
nearly all that relates to fire-arms as to make necessary
a comprehensive revision of the course of Ordnance and
Gunnery, established by the late Colonel James G. Benton
in 1861, and modified from time to time by his successors on
the Academic Board.
The subject has outgrown the limits of the small encyclo-
pedia in which Benton comprised all that was then essential
for the ordinary officer, as well as for the student, to know of
the materiel of war.
It has also lost much of the stability which characterized
it when spherical projectiles were still generally employed.
The labors of men of science and the energy of inventors
are continually extending the boundaries of knowledge and
undermining positions which appear most fixed.
Therefore, instead of giving to the course a descriptiv^e
character, it appears advisable to frame it so as to present
as simply as possible such of its principles as are the most
important, and appear the best established.
By employing the short time available for this course in
teaching such principles, the student, although less familar
with existing forms and methods than after the study of the
former course, may possibly be better fitted to understand
the causes of changes in materiel which are now so frequent,
and, as his experience increases, to wisely advise the direc-
tion that such changes should take.
VI PREFACE.
The selection, enunciation and deduction of such princi-
ples in a suitable form is rather embarrassed than assisted
by the mass of specialized knowledge to be found in the
Government reports and in the periodical press. In fact,
had it not been for the admirable text-books used at the
^'''Ecole d'' Application de VArtillerie et du Genie^'' at Fontaine-
bleau, France, for a set of which the author is obliged to
superior military and diplomatic authority, it would not
have been possible for him to prepare many of the following
pages.
Graphical methods have been freely used, both to express
abstract relations and to avoid description. In order to
reheve the memory and to train the student in reading
mechanical drawings, it is intended that the more elaborate
shall be recited on from the book.
It has been attempted to give the antecedents of present
forms, briefly, but so as to indicate the general lines fol-
lowed in their evolution and possibly to anticipate the
direction in which their improvement tends. In so doing
more stress than heretofore has been laid upon the practice
of the workshops; since the history of invention shows
that this has had as much to do with the march of improve-
ment as a special knowledge of the military necessities of
any particular case.
The thanks of the author are due :
To Mr. Geo. H. Chase, of the Midvale Steel Works, Phila-
delphia, for revising Chapter XV.
To Captain Z. L. Bruff, Ordnance Department, for the
appendix to Chapter XIX, relating to the Elastic Strength
of Guns.
To Private C. August Schopper, of his detachment, for
most of the drawings used in illustration.
West Point, New York, yuly 1, 1891.
HENRY METCALFE,
Bibliography of the Principal Works Consulted.
Benton's Ordnance and Gunnery. 6th Edition.
Mordecai's Revision of Benton. Pamphlets, U. S. M. A.
McKinlay's Text-Book of Gunnery. British. 1887.
Cooke's Naval Ordnance and Gunnery. 2nd Edition.
Text Book of Ordnance and Gunnery, U. S. N, A. 1887
Noble and Abel's Experiments on Fired Gunpowder. 2 Vols, 1880.
Proceedings U. S. Naval Insiitute. Current series.
Encyclopedia Brittanica. 9th Edition.
Bloxam's Chemistry. 6th Edition.
Byrne's Metal Worker's Assistant. 1869.
Goodeve's Principles of Mechanism. 1876.
Reports of the Chief of Ordnance, U. S, A. 1872 — 1890.
Ordnance Notes, U. S. A.
Notes on the Construction of Ordnance, U. S. A. Current series.
Reports on Naval Progress, U. S. N. 1887 — 1890.
Principal French Works.
Roulin's. Poudres de Guerre et Balistique Int^rieure. 1884.
do Armes Portatives. 1885.
Pi^bourg. Fabrication de la Poudre. 1884.
do Pyrotechnic. 1884.
Jouffret. Les Projectiles. 1881.
Berthelot. Sur la force de la Poudre. 1872.
Muzeau. Effets du tir sur les affuts. 1884.
Bornecque. Armes ^ repetition. 1888.
Malengrau. L'Artillerie a I'Exposition. 1890.
Aide Memoire. Artillerie. 1887.
Referritig to Chapter XII.
Meig's and Ingersoll's Interior Ballistics, U. S. N. A. 1887.
Medcalfe and Howard. Notes on Construction of Ordnance. N0S.36&42.
The above are derived principally from Sarrau's ** Researches on the
Effect of Powder," translated in the Proceedings of the U. S. Naval
Institute. Vol. X. Whole No. 28. And from ** Researches on the
Loading of Fire Arms." 1882.
VIU BIBLIOGRAPHY OF THE PRINCIPAL WORKS CoNStJLtED.
Referring to Chapter XIV.
Abbott's Submarine Mines. i88i. Appendices.
Eissler's High Explosives. 1884.
Monroe's Notes on Explosives. 1888.
Referring to Chapter XV.
Greenwood's Steel and Iron. 1884.
Bauerman's Metallurgy of Iron. 1868.
Jean's Steel, History, Manufacture, etc. 1880.
Thurston's Text-Book of Materials of Construction. 1886.
Chernoff on the Structure of Steel. Note on Construction of Ordnance.
No. 22.
Brinell on the Structure of Steel. Note on the Construction of Ordnance.
No. 37.
Referring to Chapter XVI.
Proceedings U. S. Naval Institute. No. 56. 1890.
Ordnance Construction Notes, 28, 49.
Referring to Chapter XVII.
Ordnance Construction Note, 26.
Refe'^ring to Chapter XIX.
Ordnance Construction Notes, 9, 19.
Referring to Chapter XX.
Bruff 's Ballistics. 1885.
Ingalls' Exterior Ballistics. 1886.
Referring to Chapter XXX.
Glennon's Accuracy and Probability of Fire. 1888.
REMARK. — The unusual method of paging adopted in this work is
intended to facilitate its revision, since new chapters can be inserted with-
out disturbing the sequence of the following pages.
INDEX
The heavy figures refer to the number of the chapter, and the lighter
figures to that of the page.
Abbott's experiments, 14, 1.
Abbreviations, 1, 4.
Abel, gun cotton, 14, 10.
Absolute error, 30, '24; force of
gunpowder, 9, 6.
Accidents, fuzes, 18, 19; gunpow-
der, 4, 1; high explosives,
14, 1.
Accles feed, 29, 6.
Accuracy of lire, 30, 5; estimated,
30, 23, 35.
Acoustic telemeters, 30, 11.
Air, combustion in, 8, 2, 10, 3, 4, 12,
3; packing, 7, 4, 21 , 7; re-
sistance of, 16, 1, 20, 8; spac-
ing, 11, 14; trajectory in, 20,
18.
Aluminium in steel, 15, 20.
Ammonium nitrate, 3, 7.
Ammunition and arms, relation, 27,
1; chest, 22, 28; rapid fire,
29, 18, 20; small arm, 27, 9,
28, 19; supply of, 2S, 17.
Ancient cannon, 13, 1; carriages,
i8l, 20; gunpowder, 13, 2.
Analysis of gunpowder, 2, 10, 9, 2,
11, 29.
Angle of fall, 20, 37, 30, 35; of
draught, 24, 3.
Animal power, 24, 1, 3, 28, 2.
Animate objects, 10, 23; areas,
30, 48.
Annapolis armor tests, 16, 43.
Annealability, 15, 23.
Annealing, 15, 38, 51, 52, 57; vrater,
15,54.
Anvils, forging, 15, 44. 46; for
])rimers, 27, 4.
Armor, kinds of, 16, 36; piercing
shell, 16, 20, 29, 21; penetration
of, 16, 36; test for projectiles,
17. 18.
Arms and ammunition, relation, 27, 1.
Artillery carriages, 22, 1; system
of, a 1,3.
Assembling cannon, 16, 58.
Axle, 22, 24.
B.
Back gear, 17, 12.
Backing, armor, 16, 37.
Back rest, 17, 13.
IJallistics, interior, 5, 1; exterior,
20, 1; coefficient (gunpowder)
12, 13, 28. 21; projectile,
16, 2, 20, 11, 23; formulae, 20,
28, 47; tables, 20, 27. 53.
Balloting of projectile, 16, 15.
Bands, carrying, 4, 5; rotating,
16, 12, 15, 17,2,15.
Barbette carriage, 22, 2, 23, 5.
Harlow's law, 19, J, 4.
Barrels, mixing, 4, 5; tumbling,
4, 4; small arm, 28, 2.
Bashforth, experiments, 20, 9;
target, 6, 15
Basic process. 15, 19, 35, 37.
Batteries, electric, 6, 15, 18, 5.
Bayonet, 26, 1.
Beaten zone, 30, 49.
Belleville springs, 22, 19, 23, 4.
Bellite, 14, 16.
Belts, 17, 12.
Benton velocimeter, 6, 3.
Berdan telemeter, 30, 15; primer,
27,4.
Berihelot's theory, explosives, 2, 3.
Bessemer process, 15, 32, 35 j »»«
ind: X.
Bickford fuze, 18, 2.
Blacking arms, aS, 29.
lilack wash, l"?, 3.
Blasts, size of, 14, 2.
Blasting fuze, 18, 2; powder, 8,
7, 9, 9, 2.
Blending gunpowder, 4, 13.
Blister steel, 15, 14, 30.
Blooms, 15, 43.
Blow holes, 15, 21.
l?o]t guns, 88, a.
Bomford's experiment, 7, 15.
Bore, rocket, 16, 44; and parts 1, 1.
Boring, 17, 13.
Bormann fuze, 18, 9.
Boxer shrapnel, 16, 31, 32.
Box magazines, 88, 11.
Brakes, 22, 11, 18.
Brinell's experiments, 15, 49.
Brgger's chronograph, 6, 10.
Breaching, 14, 19, 16, 20.
Breech, 1, 2.
Breeching, 24, 7.
Breech loading, advantages of, II, 16,
13, 2, 28, 1; projectiles,
5, 3, 16, 14; small arms,
28,5.
Broad well ring, 21, 7.
Bronze, 15, 14, 20, 24, 19, 12;
quenched, 15, 22.
Browning arms, 28, 29.
Blown powder. ( See Cocoa.)
Bruce feed, 29, 5.
Brug^re powder, 1 4, 18.
Buffers, 23, 14.
Buffington brake, 22, 19, 23, 2;
carriage, 23, 1.
Built up guns, 19, 12,22.
Bullet, manufacture, 27, 8; small
caliber, 28, 2, 20.
Burden of ammunition, 28, 4, 28, 18
Bursting charges, 14, 7, 19, 16, 20, 26,
32, 19, 17, 29, 17.
Butler projectile, 16, 13.
Buttofrifle, 28, 3.
C.
Caisson, 22, 29, 23, 2.
Cake powder, 13, i,
Caking, 16, 20.
Caliber, 1, 1; influence of, 16, 7,
17; small arm, 28, 2.
Canet system, 21, 13.
Canister, 16, 23, 25, 28, 82, 28.
Cannelures, 27, 8.
Cannon, 1, 1; B. L., 5, 3, 13, 2;
construction of, 19, 1, 22;
dimensions of, 13, 25, 21, 22;
disabling, 14, 20; metals, 15,
13, 24; M. L , 6, 3, 13, 2, 21,
4; nomenclature, 1, 1;
proportions of, 5, 2, 19, 46;
varieties of, 21, 1.
Carbine, 28, 1.
Carbo-hydrates, 11, 28.
Carbon, cement, 15, 18, 48; hard-
ening, 15, 18, 48; states of, 15,
48; in steel, 15, 18.
Carbonizers, 15, 28, 32, 36.
Carcass, 16, 22.
Carriages, artillery, 22, 1.
Cartridge, anvil, 27, 4, 5; cor-
roded, 27, 6; limit of size, 29,
IS; manufacture of, 27, 6;
metals, 27, 5; origin, 87, 1;
resizing, 27, 6,
Case hardening, 15, 27.
Case shot, 16, 18, 23.
Castan's powder, 4, 12.
Casting, 17, 1; cannon, 15, 58, 19,
12; ingots, 15, 33, 56; steel,
15, 42.
Cast iron, 15, 24; projectiles,
16, 5, 6.
Cavity in shells, 16, 18, 22.
Cellular theory, 15, 21.
Cement carbon, 15, 18, 48.
Center of impact, 30, 23; marks,
17, 13.
Centering projectile, 16, 12.
Central fire cartridge, 27, 4.
Chamber, 1, 1, 5, 3.
Change gear, 17, 12.
Charcoal, brown, 3, 5, 4, 14, 11, 28 ;
material, etc., 3, 1; pre-
paration, 3, 2; properties, 3,
4; — spontaneous ignition, 3, 4.
Cbase, 1, 3r
INDEX.
Chassis, 32, 2.
Chauvenet's table, 30, 36.
Chest, ammunition, 32, 28.
Chi (x), coefficient, 11, 20, 13, 28;
factors of, 13, 29; maximum
value of, 13, 31.
Chilled iron, 16, 5, 17, 6, 9, 14.
Chlorates, 3, 7, 14, 19.
Choice of formulae, Sarrau, 13, 6.
Chromium in steel, 15, 20.
Chronograph, Le Bouleng6, 6, 6.
Chronoscope, 6, 13.
Chuck, lathe, 17, 13.
Clips, 33, 9, 33, 6
Cluster, 16, 23.
Cocoa powder, manufacture, 4, 13 ;
theory, 11, 27.
Coefficient, ballistic, 13, 13, 16, •?, 30,
11, 23 ; of efficiency, 30, 52 ;
of elasticity, 16, 4, 10, 19,9,
22; internal ballistic, various,
11, 19; Wertheims, 19, 2, 3, 25.
Cold and heat, on high explosives,
14, 6; rolling, 15, 24, 42;
shuts, 15,44.
Collective fire, 30, 48.
Combination fuze, 18, 6, 15.
Combustion, condition of, 3, 4; in
air, 8, 2, 10, 1; in gun, 8, 2,
11, 1, 4; rates, 8, 2, JO, 3, 13,
3; volume, 11, 1.
Commercial values, 3, 9, 14, 2, 31, fi.
Common properties, high explosives,
14,2.
Communicating fire, 18, 1.
Component parts of arms, 38, 2;
of ammunition, 37, 8.
Composition of gunpowder, 3, 10, 9, 2.
Compound cylinder, strength of, 19,
14, 33.
Compressive projectiles, 5, 3, 16, 14.
Concrete powder, 4. 11.
Concussion fuze, 18, 11.
Condie's hammer, 15, 46.
Conditions of loading, 13, 16.
Cone of dispersion, 16, 23, 26, 30, 49;
pulley, 17, 11.
Constants, physical, 34, 2, 38, 16;
Constitution of steel, 15, 16.
Converted guns, II, 21, 19, 8, 31, 3,
5, 38, 15,
Conversion of gunpowder, 3, 1;
rate of 8, 3, 10, 2, 13, 3; phe-
nomena of, 8, 1.
Cooling, 15, 21, 49.
Cope, 17, 5.
Cores, 17, 4, 8, 11.
Coring, 15, 56.
Corning mill, 4, 11, 13. 3.
Counter recoil, 33, 18; shaft, 17,
12
Cradle, 35, 2.
Cranes, 1 5, 33,
Crank axle, 33, 29; kinds of, 39, 7.
Crozier's deduction, 19, 27; gun,
19, 18.
Crucible steel, 15, 31.
Crusher gauge, 7, 4.
Crystallization, 15, 21.
Cube, elastic, equilibrium, 19, 25.
Cubic law, 30, 12, 16.
Cup-anvil, 37, 4.
Cupola furnace, 15, 25.
Curvature of cutting arms, 36, 3.
Cutting arms, 36, 2; speed, 17, 12.
Cut-ofl", 38, 11. *
Cylinder, elastic, equilibrium, 19, 26,
31; gauge, 17, 17; strength
of, 16, 19, 19, 6, 31, 33.
Damascus steel, 15, 55.
Dangerous fragment, 16, 19 ;
space, 1, 3, 30, 39, 43, 49, 38, 4 ;
zone, 30, 49.
Dank's furnace, 15, 29.
De Bange gas check, 31, 8.
Definitions, general, 1, 1.
Deformation, process of, 7, 3.
Delayed action fuze, 18, 19.
De Marre, formula for armor, 16,40.
Demolition, 14, 19.
Density, gravimetric, 9, 3 ; of
loading, 9, 4, 12, 11, 14, 13, 1;
sectional, 16,1; — spherical, 16,6.
Departure, angle of, 30, 2, 45j -i— ™»
liue Of, 20, 1,
INDEX.
Depression range finder, 30, 14.
DesignoUe powder, 1*, 17.
Detachable magazine, 38, 11.
Detonation, 2, 3, 4, 14, 3; sympa-
thetic, 8, 5.
Detonator, 3, 5, 14, 3, 18, 3; tube,
18,2.
Development of small arms, 28, 17.
Deviations, 80, 4, 30, 6, 23; causes
of, 30, 6.
Dimensions of cannon, changes in,
19, 27, 37.
Dirigibility, 29, 13.
Disabling cannon, 14, 20.
Disappearing carriage, 83, 13.
Dish of wheel, 23, 24.
Disjunctor, 6, 4, 7.
Dispart, 1, 2.
Dissociation, 3, 1.
Distance, estimation of, 30, 10. ,
Drag, 17, 5.
Draught, angle of, 34, 3; horse,
34, 1; of patterns, 17, 4.
Drawn cartridge, 37, 7.
Drift, 30, 4, 30, 8.
Drill cartridge, 39, 20.
Drop test, 15, 15.
Drying gunpowder, 4, 12.
Dog, lathe, ir, 13.
Ductility, 15, 11.
Dusting gunpowder, 4, 13.
Dynamite, 14, 4, 13.
E.
Early cannon, 13, 1; carriages,
31, 20; shrapnel, 16, 30;
fuzes, 18, 7, 8.
Eccentric turning, 38, 29.
Economy, coefficient of, 11, 19.
Effective work of gunpowder, 11, 11.
Effect, factor of, 11, 11, 21.
Efficiency of fire, 30, 52.
Elasticity, 15, 3, 11; coefficient of,
15, 4, 19, 22; varying, 19, 9.
Elastic limit, 15, 4, 19, 22; choice
of, 19, 33; gtrength of guns.
Electric batteries, 6, 15, 18, 5;
primers, 18, 4.
Electro-welding, 15, 23, 17, 15, 19, 19.
Elevation, angle of, 30, 1.
Emergency powder, 8, 4.
Emmensite, 14, 17.
Energy, 3, 6, 5, 1, 16, 1, 18, 30, 22;
of recoil, 19, 19, 33, 4, 38, 16, 39,
1; of rotation, 16, 3; waste
of, 9, 10, 11, 8.
Engelhardt buffer, 33, 18.
Envelope of cluster, 16, 23; of tra-
jectory, 30, 6.
Equilibrium, equations of, 19, 25, 27.
Erosion of gun, 9, 13, 19, 20.
Errors, 30, 6, 22, 24.
Estimation of distances, 30, 10.
Eta iv), 11, 19.
Eureka projectile, 16, 14.
Eprouvette, 7, 2, 9, 5, 13, 3.
Expanding projectile, 16, 13.
Expansion volume, 11,1; volumes
of, 11, 12.
Experiments, rule for, 9, 1.
Exterior ballistics, definitions, 30, 1.
Explosion, 5i, 1; orders of, 3, 2, 4;
Berthelot's theory, 3, 3;
temperature of, 9, 8.
Explosive compounds, J8, 10;
gelatine, 14, 15; high, 3, 10,
14, 1; military, 3, 9; mix-
tures, a, 9; reactions, 3, 3; ^—
strength of, 2, 6; value of, », 8.
Eye, error of, 30, 7.
F.
Face plate, 1 7, 11.
Facings, 17, 3.
Factor of effect, 11, 11, 21.
Fall, angle of, 30, 37, 30, 35.
Feed case, 39, 5 ; of machine
guns, 39, 5, 12; screw, 17, 12.
Fermeture, cannon, 31, 9, 15; small
arms, 38, 5.
Ferreous metals, 15, 13, 24.
Ferro-manganese, 15, 28j ^UiQOn,
15,28,
INDEX.
Field cannon B L., 21, 17;
M. L., 81, 4; mortar, 31, 17;
sight, 30, 3,
Final velocity, 20, 17.
Finishing projectiles, 17,10.
Fire, angle of, 20, 5, 22, 9; arms,
1, 1; classification of, 20, 5;
line of, 20, 5; plane of,
20, 4; works, 14, 1<J.
Firing, 2, 2; gunpowder, 8, 1;
high explosives, 14, 3.
Fiske range finder, 30, 15.
Fixed carbon, 16, 48; magazines,
28, 12.
Flagler fuze, 18, 17.
Flasks, 17, 5, 8, 22, 3.
Flatness of trajectory, 1, 3, 20, 23,
40, 28, 20.
Flow of metals, 15, 11, 87, 7.
Folded head, 27,3.
Follow-board, 17, 5.
Food and feed of arms, 27, 1, 29, 12.
Force, 2, 7, 9, 7, 11, 2!), 12, 29, 14, 5.
Forcite, 14, 14.
Forging, 15, 45, 53; cannon, 16,
56; press, 16, 47.
Fork, establishing, 30, 21.
Form of cannon, 6, 2, 9, 13, 13, 2, 19,
6, 46, 21, 1.
Founding, 17, 1.
Fractures, 15, 20, 49.
Free carbon, 15, 48.
French fuze, 18, 13, 16; system,
21 , 10.
Freyi-e gas check, 21, 7.
Friction checks, 22, 11; clutch,
22, 12; .primers, 18, 3.
Fioloir, formula for armor, 16, 38.
Fulminates, 2, 10, 14, 18.
Fulmi-bran, 14, 11.
Functions, ballistic, 20, 27; experi-
mental, 9, 1, 5; independence
of, 9, 1, 16, 34, 18, 16, 19, 16, 21, 2,
19, 22, 22, 23, 24, 6, 26, 3, 4, 27, 4,
28, 4, 15, 29, 4, 8, 15, 24.
Fundamental laws, gun construction,
19, 29.
Furnaces, 15, 25, 29, 39, 45.
Fusibility, 15, 22.
Fusse, principles of, 16, J8, 28, la, 7.
Gadolin's law, 19, 9, 20,44.
Gardner gun, 29, 7.
Gaseous fuel, 16, 38.
Gas checks, 7, 3, 13, 2, 21, 6.
Gate, 17, 9.
Catling gun, 29, 2.
Gauging, 4, U, 17, 17, 28, 25.
Gautier range finder, 30, 18,
General coeflicient, gunpowder, 11,
20, 12, 28.
Gerdon fermeture, 21, 15.
Giant powder, 14, 13.
Gin, 26, 1.
Glazing gunpowder, 4, 12.
Gordon range finder, 30, 20.
Graining gunpowder, 4, 11, 13, 3.
Grains, diameter of, 10. 2, 12, 4.
Granulation of gunpowder, 4, 10.
Grape shot, 16, 23, 25.
Gravimetric density, 9, 3.
Grazed zone, 30, 49.
Grenades, 16, 20.
Gribeauval carriage, 32, 25.
Grinding, 1.5, 21, 17, 14.
Ground, slope of, 30, 51.
Guide, rocket, 16, 45.
Gun, 1, 1; combustion in, 8, 2, 11,
1, 4; form of, 5, 1; lift,
25,1.
Gun construction, theory, 19, 11, 23;
Itractice, 15, 56.
Gun cotton, 14, 2, 8 ; detona-
tion of, 2, 6.
Gunpowder, adapted to gun, 11, 7, 24,
12, 16, 32, 13, 3, 6; advan-
tages of, 2, II; characteristics,
12, 2, 22; composition of, 2, 10,
9,2; concrete, 4, 11,16,21;
fiat, 4, 12, 13, 5; Fossano, 13,
5; history of, 13, 1; hexag-
onal, 13, 5; ingredients, 3,1;
machinery, 4, 2; manu-
ficture, 4. 1; modern, 13, 6;
modulus of qaickness, 12, 10,
29; — pebble, 4, 12, 13,5; pris-
matic, 4, 15, 10, 4, 11, 6, 13, 4, 6;
products of, 2, 10, 9. 6, II, 29;
-^reaction, a, loj — KodmaB's,
INDEX.
13, 3; small caliber, «7, 9, 2S,
21, 22; smokeless, 3, 7, 14, 8,
15, 88, 22; sphero hexagoual,
13, 5; work of, 11. 10.
Gustavus Adolphus, 27, 1.
Hale rocket, 16, 46.
Hall rifle, 87, 2.
Hammers, 15, 45.
Hand arms, 36, 1
Hardening, 15, 22, 52; carbon, 15,
15, 48; strains, 15, 55.
Harness, 84, 6.
Heat of gunpowder, ^, 6, 9, 7;
waste of, 9, 10, 1 1, 8.
Hebler, system, 88, 19.
Helhofite, 14,16.
High explosives, 8, 10, 14, 1;
for bursting charge, J6, 21;
use of, 14, 7, 19.
History of ammunition, 87, 1;
of gunpowder, 13, 1; of rifling,
16, 8; of shrapnel, 16, 30;
of small arms, 87, 1, 88, 1, 16
Hitting, probability of, 30, 27, 35, 43
Hollow of wheel, 548, 24.
Hooke's law, 19, 22.
Horse and harness, 84, 1.
Hotchkiss ammunition, 89, 20;
brake, 88, 12; field carriage,
89, 20; fuzes, 18, 14; guns.
81, 16, 17; mounts 89, 1;
rapid fire gun, 29, 21; revolv-
ing cannon, 89, 14; projectile,
16, 15, 17.
Housing, pressure gauge, 7, 4.
Howitzer, 1, 1; siege, 81, 18.
Hydraulic bufier, 88, 14, 83, : ;
forgingpress, 15, 47; Jack, 85,
1; motor, 4, 9, 15, 15, 33, 34, 47,
17, 14.
Hydro pneumatic carriage, 88, .18.
Hypothesis, Barlow, 19, 2; Noble's,
9,8.
I.
Ignition of gunpowder, 8, 1; and
infl^mmAtioa iu guns, 1 1, 18.
fuze.
Igniting charges, 18, 5.
Impact, center of, 30, 23;
16, 18, 18, 6, 11.
Immovable layer, 7, 1, 11, 9
Incendiary projectiles, 16, 22.
Increasing twist, J6, 9, IJ, 15.
Incorporation of gunpowder, 4, 7, 16,
44.
Independence of function, 9, 1, 16,
34, 18, 16, 19, 16, 81, 2, 19, 22, 88,
23, 84, 6, 86. 3, 4, 87, 4, 88, 4, 15,
89, 4. 8, 15, 24.
Inertia igniter, 18, 10, 16, 17.
Inflammation of gunpowder, 8, 1;
prism, 16, -21.
Ingots, 15, 34; metals, 15, U.
Initial tension, 19, 11, 23.
Initial velocity, 1, 2.
Inspecting instruments, projectiles,
17, 17.
Interchangeability, 88,25.
Internal strain, 15, 21, 55, 19, 12.
Interrupted screw, 81, 11.
Interrupter, 6, 12.
Interstitial volume, 9, 3.
Iron castings, 15, 24, 26, 27.
Judson powder, 14, 14.
Jump, 80, 2, 3.
Kalchoids, 15, 14.
Kinetic measures, 7, 9, 16.
King carriage, 8Si, 13.
Krupp fuze, 18, 15; gun, 15, 15,
81. 6, 9; process, 15, 19;
steel, 15, 15, 32.
Lathe, 17, 11;
13.
Lance, 86, 1.
Lands. 1,2.
Leather, 84, 9.
Lead, projectiles, 16, 5, 24
Lead of wheel, 88, 24.
Lebel powaer, 14, 18.
variations of, 17,
INDEX.
Le Bouleng6 Telemeter, 30, 11;
chronograph, 6, 6.
Lee rifle, 38, 7, II.
Lemoine brake, 33, 19.
Length of bore, 5, 2, 7, II, 11, IJ, 13,
2, 19, 47.
Levers in guns, 27, 6, 28, 6.
Light balls, 16, 22.
Limber, 23, 27, 23, 2; chest, 22,
28
Limiting values of pressures, 19, 39.
Line of departure, J*0, 1; of metal,
1, 2; of signt, ao, 1.
Liners, 19, 20.
Liquation, 15, 16.
Loam, 17, 3.
Lock, Springfield, 28, 16,
Longitudinal stress, 19, 16, 30.
Longridge gun, 19, 19.
M.
MacDonald, Hale rocket, 16, 45.
Machines, artillery, 25, 1; guns,
21, 1, 29, I, 12.
Magazine arms, 27, 3, 28, 9, 13, 14.
Maitland formula for armor, 16, 38.
Malleability of metals, 15, 23.
Malleable castings, 15,27.
Mandreling, 15. 22, 19, 11.
Mandrels, forging, 15, 47.
Manganese in steel, 15, 19.
Mannlicher rifle, 28, 12.
Manometric balance, 7, 8.
Manufacture of ammunition, 27, 6;
of fuzes, 18, IS; of gun-
powder, 4, 5; of projectiles,
17, 1; of small arms, 28, 24.
Marking gunpowder, 4, 13.
Matches, 18, 1.
Maxim aut. machine gun, 29, 8;
rapid fire gun, 29, 25.
Mayewski's experiment, 7, 9.
Mean error, 30, 24, 33; point of
impact, 30, 23; trajectory, 16,
23, 30, 6.
Mechanism, small arm, 28, 5.
Megagraph, 6, 7.
MeUing^, 15,24, n,6.
Metals for cartridges, 27, 5; ord-
nance. 16, 13; physical prop-
erties of, 15, 13; useful prop-
erties of, 15, 15.
Metallic cartridges, 27, 2.
Micrograph, 6, 8.
Mildness, coeflicient of, 11, 19.
Military explosives, 2, 9.
Mill cake, 4, 8; gunpowder, 4, 1;
train, 15, 43; universal,
15, 43.
Milling, 17, 13,28,28.
Mi lis metal, 15, 20.
Mixing gunpowder, 4, 7, 16, 44.
Modulus of elasticity, 15, 4, 19, 22.
Moistening gunpowder, 4, 7 ;
molds, 17, 2
Molding, 17, 1, 10; composition,
17, 2; tools, 17, 6.
Molded gunpowder, 4, 10 ;
press for, 4, 15.
Moncriefl carriage, 22, 13,
Morse cartridge, 27, 5, 28, 22.
Mortar, 1, 1, 21, 17, 19,22; car-
riage, 23, 7; fire, formula; for,
20, 6, 8; fuze, 18, 9; wagon,
22, 28.
Mounts, for rapid fire guns, 29, 18.
Mountings, email arm, 28, 5,
Mu ifi), 11, 19
Mule, 24, 1.
Muzzle loading projectiles, 5, 3, 16, 12.
N.
Napoleon gun, 21, 4.
Nasmyth hammer, 15, 45.
Natural line of sight, 30, 2.
Nave, 22, 22.
Nickel armor, 16, 43; in steel,
15, 20.
Nitrates, 3, 6, 12,29.
Nitre, 3, 6.
Nitro-benzine, 14, 15; glycerine,
14, 11.
Niven's method, 20, 25.
Noble's gauge, 7, 4; experiments,
7, 16, 9, 1; — an(i Abel's law,
9,8,
INDEX.
Nolan range finder, 30, 20,
Non-metallic cartridges, fil, 2.
Non-recoil guns, as, 18, 29, 1 ;
mount, 29, 19.
Nordenfelt gunpowder, 4, 15;
machine gun, 89, S; rapid fire
gun, 29, 24.
Nucleus, 30, 6.
Number of grains varied, 10, 2.
Oblong projectiles, advantages of, 16,
4.
Obturating primers, 18, 4.
Oil hardening, 15, 53, 57.
Open hearth process, 15, 37;
steel, 16,14,32.
Orders of explosion, 3, 2, 4.
Ordnance, I, 1.
Origin of motion, .1,10.
Oxidation, rate of, 15, 37; scale
of, 16, 17.
Oxydizing agents, 3, 6.
P.
Pack horse, 84, 1.
Palliser gun, ai, 5. '
Parallax, 30, 11.
Parrott gun, 21, 5 ; i)rojectile,
16. 12.
Parting plane, 17, 4; sand, 17, 3.
Passive resistances, 11, 8.
Patterns, 17, 3, 7.
Pebble powder, 4. 12, 13, 5.
Peep sight, 30, 4.
Percussion caps, 18, 2; fuze, 18,
11.
Pemot furnace, 15, 30, 41.
Petroleum fuel, 15, 38.
Phi dash(g)), 20, 22, 37, 50.
Phosphorus in steel, 15, 19.
Physical constants, 24, 2, 28, 17;
properties, 15, 1, 12, 20, 57.
Pi (FT), coj^fficient, 11, 27, 12, 29.
Picric acid, 1 4, 17.
Piemonte S. S., 29, 17,
Fiutles, ^^, 9, 36..
Piping, 15, 21.
Plane table, 30, 14.
Platforms, '4a, 19.
Pointing, 20, 1, 30, 1.
Porter bar, 16, 56.
Ports, 22, 14.
Potasaum chlorate, 3, 7, 14, 16, 19.
Potential, », 6, 9, 7; work, 2, 6,
II, 9, 15, .
Pouring, 17, 7.
Powder mills, 4, 1.
Pratt range finder, 30, 17.
Precautions in manufacture of gun-
powder, 3, 5, 4, 1.
Premature explosions, 18, 19, 21, 14,
28,6.
Preponderance, 1, 2, 22, 8.
Press cake, 4, 7; forging, 16, 47;
powder, 4, 9, 15.
Pressure curve, 9, 13, 11, 3, 12, 8,
19, 46.
Pressure, exterior limits of, 19, 39;
formula;, Sarrau, 12, 8, 13;
gauges, 7, 1, 5; in gun. Noble
and Abel, 9, 11; ■ high explo-
sives, a, 8, 14, 4; piston, mass
of, r, 6.
Primers, 14, 3, 18, 1, 3.
Probability of fire, 30, 27.
Probable error, 30, 32; rectangle,
30, 34; zones, 30, 33.
Products of gunpowder, 2, 10, 11, 29;
of high explosives, 2, 2, 14,
4. 9, 12.
Profiling, 28, 28.
Profile of i)rojectile, 16, 16, 20, 9.
Progressiveness, 10, 3, 11, 19.
Progressive range finding, 30, 21.
Projection, angle of, 20, 2.
Projectiles defined, 16, 1; form
of, 5, 3; manufacture of, 1 7, 1;
proof of, 17, 16, 18.
Proposed magazine arm, 2S, 13.
Proportions of cannon, 5, 2, 9, 13, 13,
2, 19, 6, 46.
Puddled steel, 15, 30.
Pulls, 15, 44.
Pulverizing gunpowder, 4, 6,
Funching armor, 16, 36,
iJ^i)E5t.
Quadrant an^le, 20, 2.
Quenching 15, 22, 49.
Quickness of gunpowder, 11, 7,24, 12,
10, 12, 29.
Quick loader, 38, 13.
Quick match, 1 8, 1.
Rackarock, 14, 15.
Racking armor, 16, 36.
Radius of gun, 20, 1.
Ramsbottam's hammer, 15,47.
Range, 20, 4 ; to compute, 20, 36;
finding, 30, 10; table, 30,
8, 52.
Rapidity of lire, 27, 2; 28, 1; 29, 1, 7,
11, 16, 17, 26, 30, 61; of re-
action, 2, 8.
Rapid firing guns, 21, 1, 29, l, 16.
Reaction, gunpowder, 2, 10; gun
cotton, 14, 9; nitro-glycerine,
14, 12; rapidity of, 2, 8.
Re- annealing, 15, 67.
Recoil, angle of greatest, 22, 9; of
cannon, 11, 18, 19, 19; control
of, 22, 11; — energy of, 19, 19, 2'^,
3; extent of, 22, 7, 11, 16;
force of, 22, 5; mount, 29, 19;
periods of, 22, 3; pheno-
mena of, 22, 8; rotation due
to, 22, 8; small arms, 28, 16;
in testing metals, 15, 3;
work of, 15, 5, 22, 4.
Refining steel, 15, 52.
Regenerator, 15, 39. .
Reheating furnace, 15, 45.
Remeltlng iron, 15, 24,
Reinforce, 1,2.
Resistance of air, 20, 8, 16; of
cannon, 19, fi, 31, 3:5; passive,
11, 8; of primers, 18, 4.
Retardation, coefficient of, 16, 2.
Reverberatory furnace, 15, 25.
Revolvers, 28, 23.
Ricqs register, 7, 15.
Rifle, 28, 1.
Rifling, 1, 2, 16, 8, 28, 3, 27.
Right line method, 30, 41, 45.
Rigidity of trajectory, 20, 24.
Rimfire cartridge, 27, 3.
Rimless cartridge, 28, 23.
Riser, 17, 9.
Rockets, 16, 44.
Rodman's gauge, 7,3; gun, 19,12;
improvements in gunpowder,
13, 3; velocimeter, 6, 13, 7, 12.
Rolls, 4, 3,
Rolling mill, 15, 43; — ^ table, 17, 17.
Rotating bands, 17, 15; device,
11, 16, 16, 12, 15.
R^ation of projectile, 11, 16, 16, 12.
Rotary energy, 16, 3; furnace,
15, 37, 41.
Rotten steel, 15, 18.
Rumford's gauge, 7, 2.
Rupture of shells, 16, 19.
Russell's interrupter, 6, 13.
Saber, 26, 2.
Safe space, 20, 39, 43, 30, 51.
Saltpeter, 3, 6.
Sand, molding, 17, 3.
Sarrau, application, 12, 21, 28 ;
formulae, 12, 1; on pressure
gauge, 7, 8.
Sawyer canister; 16, 25.
Schulhofl" magazine rifle, 28, 13.
Screw guns, 21, 17; interrupted,
21, 10.
Sea coast cannon, 21, 20; car-
riage, 23, 5; fuze, 18. 9.
S6bert's projectile, 7, 10; veloci-
meter, 6. 13, 7, 13.
Sectional density, 16, 1, 28, 21.
Segment shell, 16, 33.
Segregation, 15. 16, 59.
Sensitiveness of high explo.sives, 14, 2.
Set of metal, 15, 3; of wheel, 22,
24.
Shafts, 22, 28.
Sheaf of dispersion, 16, 23, 30, 6.
Shearing plane, 27, 4.
Shear steel, 15, 30
Shells, 16, 18; bursting charges,
14, 7, 19, 16, 20, 33, 19, 17.
10
1NDE5^.
Shields for guns, 16, 41, 23, 6.
Shock, explosion by, 8, 2, 14, 3, 7, 12,
15, 16, 16, 21, 18, 11.
Shortening bore, 7, y.
Shrapnel, 16, 23, 26; early, 16, 30;
fire, 16, 34.
Shrinkage in cannon, 15, 21, 58, 19,
12, 15, 23, 41.
Shuts. 15, 44.
Side-box, maxim, 29, 27.
Siege cannon, 21, 17; carriage,
«3, 3.
Siemen's furnace, 15, C9; regene-
rator, 16, 3!).
Sights, 20, 1, 28, 4, 20, 30, 1;
angle of, 20, 2; field, 30, 3;
heavy guns, 30, 3; line of,
20, 1; plane of, 20, 4;
radius, 20, 1; small arm, 28, 4.
Signal time, 6, 1, 12.
Silico-Spiegel, 15, 18, 28.
Silicon as fuel, 15, 35; in steel,
15,18.
Similitude, principle of, 1^, 14.
Sinclair check, 22, 12.
Singletree, 22, 27, 24, 5.
Sinking head, 15, 34, 58, 17, 10, 15.
Single cylinder, strength of, 19, 6, 31.
Size of grain, 10, 2, 11, 4.
Slide rest, 17, 11.
Sling cart, 25, 2.
Slow match, 18, 1.
Small arms, 1, 1, 28, 1; ammuni-
tion, 27, 1, 9; manufacture of,
28, 24.
Small caliber, 28, 2, 20.
Smokeless gunpowder, 3, 7, 14, 15,
28, 22.
Soaking pits, 15, 43.
Sodium nitrate, 3, 6.
Solid head cartridge, 27, 5.
Solid shot, 16. 18.
Special irons, 15, 27.
Specific gravity of gunpowder, 9, 3;
of iron, 16, 24.
Specific volume, 2, 7, 9, 3, 7.
Spheres of action, 14, 5.
Spherical case. 16, 31; density, 12,
31, 16,6, 28,21.
Spiegeleisen, 15, 28.
Spindles, lathe, 17, 11.
Sprengel mixtures, 14, 16.
Springfield rifle, 28, 15.
Stationary carriages, 2'4, 1.
Stadia, 30, 13.
Static measures, 7, 2
Steam, comparison to, 11,1; test,
17,17.
Steel castings, 15, 42; cast can-
non, 15, 58; classification of,
15, 13, 18; composition of, 15,
17; constitution of, 15, 16;
manufacture of, 15, 30; me-
chanical treatment of, 15, 4 ;
molecular treatment of, 15,48;
projectiles, 16, 6; projectiles,
manufacture, 17, 14; proper-
ties under stress, 15, 22; struc-
ture of, 16, 20, 49; working
properties, 15, 22.
Stock, cannon, 22, 3, 25; rifle, 28, 3.
Stone projectile, 16, 5.
Store wagon, 22, 29.
Strain diagram, 15,3,8; equalizing,
19, 9, 19, 23; internal, 15, 21,
55, 19, 12; as function of
radius, 19, 3, 29; on gun, 5, 2,
16,3, 19,1.
Strength of cannon, 5, 1, 2, 1 9, 6, 31, 33;
of explosives, 2, 6; of gun
construction, coeflicient for, II,
21.
Stress and strain, 16, 1, 19, 22; in
guns, 5, 2, 16, 3, 19, 1.
String measure, 30, 24.
Structure of projectiles, 16, 17.
Studded projectile, 16, 12.
Successive means, method of, 30, 21;
shortening of bore, 7, 11.
Sulphur, 3, 1; in steel, 15, 20.
Supply train, '-i'-i, 29.
Surface of gunpowder, 8, 1, 10, 1.
Sweep molding, 17, 3, 5
Swiss method, 30, 27.
Sword, 26, 1.
Sympathetic detonation, 2, 5.
System of artillery, 21, 3; at rest,
etc, 19, 13, 36.
INDEX.
11
Tarage, 7, 7.
Targets, animate, 30, 48; —— comput-
ing, 30, 26; velocity, 6, 14.
Team, arrangement of horses, 24, 5.
Telescopic sight, 30, 3.
Telemeters, 30, 11,
Temperature of ignition, 8, 1, 14, 3;
of explosion, 2, 8, 9, 8;
scale of, 1, 3.
Tempering, 15, 52.
Tenacity, 15, 10.
Testing cannon metal, J 5, 57;
machines, 16, 1,5; projectiles,
17, 18.
Test piece, form of, 16, 2; record,
15, 2, 8.
Thickness of cannon, 5, 2, 9, 13, 19,6,
19, 45, 46.
Thrusting arms, 86, 1.
Thurston machine, 15, 6.
Tilted steel, 15, 30.
Time of flight, 30, 40, 41, fuze, 16,
18, 18, 6, 10; limits, 6, 8;
of maximum, 13, 11.
Tire rolling, 15, 44.
Tolerance, 4, 11, 17, 17.
Tonite, 14, 9.
Torpedo shells, 14, 8, 16, 20, 31, 18.
Torsional testing, 16, 6.
Trajectory in air, 30, 18; curva-
ture of, 1, 3, 30, 23; elements
of, 30, 30; flatness of, 1, 3. 30,
23, 40, 38, 20, 30, 35, 30; mean
radius of curvature, 30, 23;
rigidity of, 30, 24; in vacuo.
30,6.
Traveling trunnion bed, 33. (.
"Treatment" of cannon, 15, 57.
True mean error, 30, 33, 41.
Trunnions, inclination of, 30, 2.
Tubular magazines, 38, 10.
Tuning fork, 6, 12, 7, 13.
Tumbling barrels, 4, 4; of pro-
jectiles, 16, 3.
Turning angle, 33, 25.
Twist, 10, 9,
U.
U, path of projectile, 11, 10, 14, 13, 1.
Units of measure, 1, 3.
V.
Vacuo, trajectory in, 30, 6.
Value of explosives, 3, 8, 14, 2.
Variables, experimental, 9, 1.
Varying elasticity, 19, 9.
Velocimeters, 6, i, 7, 9; Benton,
6, 3; classified, 6, 2.
Velocities defined, 1, 2; final, 30,
17; formula;, 13, 5, 12;
targets, 6, 14.
Vents 11, 18, 31, 13; direction of,
18, 3; rocket, 16, 44.
Vertex, height of, 30, 36; prin-
ciple of, 30, 42.
Very's formula for armor, 16, 41.
Vesiculation, 15, 21.
Volumes of expansion, 11, 12.
Vulnerability, 30, 50.
W.
Wagon, mortar, 33. 28; store, J5J5,
29.
Washed metal, 15, 19.
Waste of energy, 9, 10, 11, 8.
Water on high explosives, 14, 5, 6;
annealing, 15, 54; cap,
18,9.
Weather, 30, 9, 30, 10.
Weaver formula for armor, 16, 42.
Weight of cannon, 6, 1, 19, 19; of
charge, Jl, 13, 15, 13, 16, 32, 38,
21; distribution of, «3, 4, 34,
2, 38, 17; of projectile, 16, 8.
Weld steel, 15, 14.
Weldability of metals, 15, 23.
Weldon range finder, 30, 16.
Wertheim's coefficient, 19, 2, 3, 25.
West Point target, 6, 15.
Whitvvorth's forging press, 16, 47;
projectile, 16, 12, 17;
steel, 16, 15, 34.
Wheel mills, 4, 7; principles <jf,
33, 21.
12
INDEX.
Wheeled carriages, 23, 2.
Wiener's powder, 4, iO.
Wiliiston harness, 24, 8.
Winchedter magazine rifle, 28, 10.
Windage, 1, 2.
Wind and accuracy, 30, 9.
Wire drawing, 15, 44; wound can-
non, 19, 17.
Woodbridge gun, 19, 18.
Woods, physical properties of, 16, 11 .
Work of gunpowder, 3, 6, 9, 7, 11, 10.
Wrapped metal cartridge, 87, 7.
Wrought iron, manufacture, 16, 29;
projectiles, 16, 5.
Zalinski gun, 10, 3, 14, 8.
Zones in collective fire, 30, 49.
Zones, probable, 30, 33.
I. — DEFINITIONS.
- 07 THr:
^TJKITEBSIT
CHAPTER I,
DEFINITIONS.
Ordnance. — A general terra usually applied only to the
material of Artillery, but embracing also all warlike stores
made according to prescribed regulations or ordinances.
Fire Arms. — Offensive weapons used to throw projectiles
by means of explosives. They are divided into —
1. Cannon. — Heavy fire arms requiring carriages to sup-
port and to transport them.
2. Small Arms, — Which can be carried by men.
Cannon are divided into —
Guns. — Or relatively long cannon. Gun is used as a gen-
eral term for all fire arms. It has probably the same root
as engine, meaning a machine.
Howitzers.. — Comparatively short cannon.
Mortars. — Very short cannon.
NOMENCLATURE.
Bore. — That part of a cannon which is bored out. It in-
cludes —
1. The cylinder or principal portion of the bore.'
2. The seat of the charge, or the part occupied by the
powder. This may be either a continuation of the cylinder
terminated by a plane or curved surface; or a cha?nder, the
diameter of which differs from tha* of the cylinder of the
bore. For breech loaders, the chamber is divided into the
powder chamber and the shot chamber.
Caliber. — The diameter of the cylinder of the bore. It was
formerly expressed by the weight of the inscribed sphere.
I. — DEFINITIONS.
For cannon, this was the weight in pounds of the cast iron
shot; for small arms, the number of leaden balls required to
weigh a pound.
Rifling. — Cutting spiral grooves in the surface of the bore,
so as to give to the projectile a motion of rotation at right
angles to that of translation.
Lands. — The ridges left between the rifle groves. The
caliber of rifles is usually measured between lands.
Chase. — The long conical portion of a cannon in rear of
the muzzle.
Reinforce. — The thick portion of the body over and imme-
diately m front of the seat of the charge.
Breech. — The mass of metal in rear of the plane of right
section at the base of the charge.
Line of Metal. — The intersection of the upper surface of
the piece by an axial plane perpendicular to the axis of the
trunnions.
Dispart. — The difference between the semi-diameters at
the muzzle and at the breech.
Preponderance. — The difference between the moments of
the weight in front of, and in rear of, the trunnions.
Windage. — This is properly the difference between the
area of right section of the cylinder of the bore, including
the grooves, and the maximum parallel area of right section
of the projectile.
It is usually expressed in linear units as the difference
between the diameter of the cylinder of the bore and the
diameter of the projectile.
VELOCITIES.
Muzzle or Initial Velocity. — Is the maximum velocity of
the projectile after leaving the piece,
t. — BEFmiTlONS.
Remaining Velocity. — Is that at any point of the trajec-
tory.
Terminal Velocity. — Is that at the point of impact.
The greater the velocity at any instant, the more flat does
the trajectory become; and, therefore, the greater is the
probability of striking a vertical object at an unknown
distance. (See note 1, page 5.)
The horizontal distance over which, under given condi-
tions, a vertical object would be struck, is called the dan-
gerous space for that object.
UNITS OF MEASURE.
Those used in English speaking countries are unfortun-
ately numerous and are apt to cause confusion.
Units of Temperature.
Throughout this work the temperatures are expressed in
degrees centigrade.
Units of Length,
Yards. — For ranges of projectiles.
Feet. — For measuring velocities and the chords and alti-
tudes of trajectories.
Inches. — For the internal dimensions of guns and for all
dimensions of their projectiles. The decimal sub-division
of the inch is generally employed.
Units of Weight,
Tons. — For cannon, 1 ton =2240 lbs.
Pounds. — For large projectiles, for their charges and for
measuring the pressures (per square inch) of the gases of
fired gunpowder.
In England, pressures are measured in tons per square
inch; in France, in kilogrammes per square centimetre; else-
where on the continent of Europe in atmospheres.
t. — MFiNitioNS.
Grains Troy. — For bullets and powder charges of small
arms 7000 grains troy=l lb. avoirdupois.
g is generally taken =32.2 lbs., which is nearly its value at
London.
Unit of Energy and Work,
Foot tons=foot pounds-r2240.
USEFUL MECHANICAL FORMULAE.
s
Uniform motion, v=-
ds
Varied motion, v— —r:
Uniformly varied motion, v=-aJ<^ a-k = a-fj h— —
%
. . dv d^s
Acceleration, af= -T- = -To- .
at dt^
Intensity of a motive force, I=Ma.
Intensity of an impulsive force, I^-^MV,
Measure of work, Q=Wh—flds,
Measure of energy, E= ^f^^
Time of oscillation of a simple pendulum, t=;rA / —
ABBREVIATIONS.
S. B. — Smooth bore.
R.— Rifle.
M. L. — Muzzle loading.
B. L. — Breech loading.
C. I. — Cast iron.
W. I. — Wrought Iron.
S._Steel.
The caliber is placed first. Example:
8 in. B. L. R. S.
1.— i>EpmiTtoNS.
15 in. S. B. C. I., etc.
W. w. — Weight of larger and smaller of two masses consid-
ered; as of piece in regard to projectile, or of projectile in
regard to charge of powder.
V. V. — Initial and remaining velocities.
p. — Intensity of gaseous pressure per unit of area.
r. d. — Radius and diameter of the cylinder of the bore, or
of the projectile according to context.
Note 1. From Michies Mechanics, Article 94, we have — = '^ ^^
See also Chapter XX, p. 22. p "v ,
!I. — EXPLOSIVE AGENTS.
CHAPTER II.
EXPLOSIVE AGENTS.
Explosion.
Is a name given to a series of phenomena resulting from
two general causes.
Causes of Explosion.
I. The rapid conversion of a solid or liquid to a gaseous
state. This conversion is accompanied by the evolution of
heat, due to the nature of the chemical reaction involved.
II. The rapid dilatation of a mixture of gases by the heat
evolved in their combination. Such explosives are not yet
generally employed in warfare and are not herein considered.
Products.
The gases evolved in conversion are principally CO2 and
CO. These result from the more or less perfect combustion
of carbon, which enters into every military explosive under
circumstances intended to facilitate its oxidation.
Dissociation.
The tendency at high temperatures of CO2 and other com-
plex products to occur in simpler forms, as CO + O, is sup-
posed by Berthelot to exert a powerful influence upon the
corresponding pressures.
Dissociation, as this phenomenon is called, whether it pre-
vents the formation of the complex product or destroys it,
increases the specific volume of the gaseous products; but,
since Mariotte's law has been proved not to hold for pres-
sures ^ of those found in fire arms, it is supposed that the
loss of heat from imperfect combination, or from work done
II. — EXPLOSIVE AGENTS.
in breaking up the molecules already formed, exceeds in its
effect upon the resultant pressure the increase of specific
volume cited. External causes may subsequently decrease
the temperature and permit recombination with a relative
increase of pressure.
It is found that, when the conversion yields a large pro-
portion of CO, the violence or sharpness of the explosion is
increased. This is supposed to be due to the rigidity or
stability of this gas against diSvSOciation.
H2 O is, by some, supposed to be subject to dissociation
at the temperatures found in explosions. (See Bloxam, Arts.
36, 68, 311, Note.)
Firing.
The proximate cause of the reaction resulting in an explo-
sion is always the absorption by some portion of the explo-
sive of heat sufficient to raise its temperature to the point
necessary to start the conversion.
The source of heat may be external; or, as in spontaneous
decomposition, internal.
The means by which the temperature of the explosive is
raised to the critical point may, in general terms, be called
firing.
Firing generally results from the transformation of kinetic
energy into heat as a result of arresting the motion of either
molar or molecular masses.
Almost all explosives may be fired by molar shock, if it be
concentrated on a mass of the explosive which is sufficiently
small. (Bloxam, Arts. 309, 434, 538).
Orders of Explosion.
The energy of molecules in motion depends principally
upon their velocity; and the external work done in stopping
them, upon their stability of composition. When an explo-
sive is fired by contact with incandescent matter, as by a
flame consisting of molecules of COg, C, etc., moving with
II. — EXPLOSIVE AGENTS. 3
relatively low velocities, the explosive is said to be ignited^
and the explosion is called low or of the second order.
When fired as by fulminate or gun cotton, the conver-
sion of which yields a large proportion of molecules of CO,
moving with a very great velocity, the explosive is said to
be detonated, and the explosion is called high or of \.\\& first
order. ■ Explosives which readily detonate are called high
explosives.
Example, Gun-cotton when —
Order.
Ignited j unconfined; burns quietly —
^ * * ' ( confined; explodes like gunpowder 2nd
unconfined ) i j vu
[ explodes with great
f violence 1st
Detonated . . . -j or
( confined;
The distinction between the two orders of explosion is
only conventional; the phenomena in practice appearing
often to partake of the nature of both orders.
This may explain certain anomalies observed in mining
and in artillery. In mines, when the charges are large, the
high pressure resulting from the initial explosion, if at a
point considerably beneath the surface of the charge, is sup-
posed to cause the detonation of the remainder. In cannon
the mixing of quick with slow powder produces a similar
effect.
BERTHELOT S THEORY OF EXPLOSIVES.
Origin of Reactions.
" Every explosion must be referred to some initial increase
of temperature transmitted from particle to particle on the
surface of an explosive wave. This wave raises successively
all portions of the explosive to the temperature of convei-
sion.
II. — EXPLOSIVE AGENTS.
Propagation of Eeactions.
Two limiting conditions are supposed to result, viz.:
1. The condition of combustion.
2. The condition of detonation.
These are progressively interchangeable in different de-
grees, according as the amplitude and velocity of vibration
of the particles forming the surface of the explosive wave
are increasing or diminishing.
Combustion.
I. The condition of combustion depends upon a reduc-
tion of temperature from the free expansion of a portion of
the gases resulting from the initial explosion.
Successive portions of the explosive will thereupon be
heated to the temperature of decomposition with a velocity
depending upon various conditions; this velocity, compared
with that of detonation, is slow.
Detonation.
II. On the other hand, the condition of detonation de-
pends upon an initial shock, too sudden (sharp) to permit of
molar motion of the particles of the explosive. It is, there-
fore, transmuted into heat which may raise the contiguous
molecules to the temperature of conversion. The result-
ing gases arc projected as a single (not periodic) explosive
chemical wave traveling throughout the successive layers of
the unexploded mass. This wave transforms its energy into
heat at each impact, and, by virtue of its acceleration, raises
each of the successive layers more rapidly to the tempera-
ture of conversion.
Origin of Orders of Explosion.
The order of the resulting explosion will depend upon the
velocity with which the reaction is propagated; /. ^., the velo-
city of the wave surface described.
The velocity of the wave surface will depend —
n. — EXPLOSIVE AGENTS.
1. Upon the molecular velocit}^ of the reaction; /. ^., the
rate of conversion under constant conditions.
2. Upon conditions which prevent the free expansion of
the gases formed.
3. Upon the mass and initial temperature of the explo-
sive; these affect the rate of cooling.
The last two conditions may be neglected when, as with
the high explosives, the first is fully satisfied.
Influence of Detonator.
It is seen that detonation depends upon a chain of causes
which results from the nature of the initial explosion. Herein
lies the importance of the nature of the detonator, its mass,
and the nature of its own explosion.
Its conversion should be rapid and evolve abundant heat.
The mercuric fulminate is the detonator which is preferably
employed. It is less violent than NCI, but yields more heat
by its explosion and also much CO.
Influence of the Explosive detonated.
Detonation depends upon the physical condition of the
explosive. Its sensitiveness generally diminishes as its den-
sity and elasticity increase, since the shock is distributed
over a greater mass."
SYMPATHETIC DETONATION.
Conditions.
The instability of the high explosives renders their con-
tact unnecessary when the continuous detonation of several
charges is desired. The maximum interval permitting ''sym-
pathetic detonation," or "detonation by influence," and the
order of this detonation, depend upon the elasticity of the
intervening medium, the mass of the primitive charge, and
the order of its explosion.
Examples.
Calling w the weight of the primitive charge in pounds,
and d the maximum interval in feet —
n. — EXPLOSIVE AGENTS.
In water, d=S w.
On a firm soil, (/=5 w.
On an iron rail, ^=10 w.
When discs of compressed gun-cotton are in contact, the
velocity of detonation is said to be over 3J miles per second
when the discs are wet, and less than 3J miles per second
when they are dry. The incompressibility of the water assists
in transferring the shock.
STRENGTH OF EXPLOSIVES.
The strength of an explosive, or its mechanical efificiency,
may be analyzed by reference to 1, its potential; 2, its force;
3, the molecular velocity of its reaction.
1. Potential.
The potential of an explosive is the maximum work
which a unit weight of it can perform. It is measured by
the product of the quantity of heat liberated by the reaction,
and the mechanical equivalent of heat; or, Q= J x H.
The potential is independent of the process of conversion,
provided it be complete and its products be constant.
In practice, these products often vary with the circum-
stances under which they are formed, so that the potential
realized will also vary.
Only a portion of the potential can be realized in prac-
tice, depending upon the volumes of the gases produced,
their specific heats, and the difference between the tempera-
tures at which they are formed and to which they are ex-
panded.
Examples.*
Theoretical potentials, in foot tons, resulting from the
conversion of one pound of each of the following sub-
stances:
* It is required that only the general principles illustrated by this and
following tables shall be committed to memory.
II. — EXPLOSIVE AGENTS.
Name. Foot Tons. Proportion.
Blasting powder 391 1.0
Cannon " 609 1.3
Sporting « 642 1.4
Gun-cotton 716 1.8 1.0
Dynamite No. 1 884 2.3 1.3
Explosive Gelatine 1,235 3.2 1.8
Nitro-glycerine 1,282 3.3 1.8
Chloride of Nitrogen 216 0.5
Anthracite coal 6,170 13.0
The greater potential of coal is due to its composition and
to there being no loss of energy expended in converting in-
to gas the compounds of oxygen contained in the other sub-
stances.
2. Force.
The force of an explosive, or the pressure per unit of area
due to the explosion of a unit of weight in a unit of volume,
may be calculated on theoretical grounds from the formula,*
In which v^ is what is known herein as the specific volume of
the gas, viz.: the volume in litres of the gases resulting from
firing one kilogramme of powder, taken at 0° C, and at the
pressure p^ of one atmosphere ; and c is the specific heat of
the gas.
But the uncertainty attending the application of the laws
of Mariotte and Gay-Lussac to such high pressures as exist
in cannon, and the doubt as to the nature and state of the
products of explosion at the epoch of maximum pressure
have caused instrumental measurements of pressure to be
preferred.
Examples.
The following table shows in round numbers the relative
force of the explosives named.
* For the deduction of this formula see page 11.
II. — EXPLOSIVE AGENTS.
The detonation of gunpowder was accomplished by mix-
ing it with dynamite.
Eelative Force.
Explosive. 1st Order. Snd Order.
Gunpowder 4.0 1.0
Gun-cotton 6.0 3.0
Nitro-glycerine 10.0 5.0
The force of a mixture of high explosives is proportional
to the sum of the products of the force of each constituent
by the corresponding fractional part of the whole mass.
A remarkable property of gunpowder (to be referred to
hereafter) is that, however its potential may vary with its
composition, the force of all compositions is sensibly con-
stant. The specific volume of the gases formed seems to
vary inversely with the quantity of heat evolved in their
formation.
3. Rapidity of Reaction.
The temperature increases with the rapidity of the reac-
tion. This depends upon the affinity between the combin-
ing molecules, and largely upon the state of aggregation
of the exploding mass, in so far as it affects the distances
between them.
In certain high explosives, the rapidity of the reaction
causes so high a temperature that the gaseous products are,
as it were, shot against the w^alls of the envelope with such
velocity that the effect seems due rather to a physical shock,
than to the elastic pressure of a confined gas. With such
explosives tamping is relatively unneccessary.
VALUE OF EXPLOSIVES.
As a general rule, the value of an explosive depends: —
1. Mechanically; upon its primitive state of aggregation, in
so far as this affects the ease of handling it in loading; also
upon its density.
II. — EXPLOSIVE AGENTS.
V H
2. Chemically; upon the value of the ratio —2 — z=iv^T^
If, when this is great, the conversion is sufficiently rapid, a
high and elastic pressure will succeed the initial shock; this
pressure will be well sustained, since the cooHng effect of
the envelope will be relatively small.
The potential of an explosive is thus seen to be the
measure of its power of sustaining a given force or pres-
sure.
Examples.
The relative importance of potential, force, and rapidity,
depends upon the use made of the explosive.
In order to burst, we use one of high force and density,
acting locally like an hydrostatic pressure.
Chloride of nitrogen detonates with such rapidity that it
may simply pulverize the surface of the envelope without
rupturing its walls.
For mining in rock or coal, blasting powder is better than
cannon powder, since the end sought is rather the rup-
ture of the envelope than the dispersion of the fragments.
Its force depends on the great specific volume of the gases
generated rather than upon their temperature.
For blasting in earth, cannon powder is better than blast-
ing powder as its potential is higher. Its diminished den-
sity, compared to high explosives, distributes the effect over
a larger area.
MILITARY EXPLOSIVES.
The principal explosives used in warfare are of two
general classes:
1. Mixtures.
Gunpowder and its like; these are more or less inti-
mate mechanical mixtures of combustibles, such as C, S, Sb,
with an oxydizing agent, generally a nitrate or a chlorate.
10 ■ II. — EXPLOSIVE AGENTS.
Explosives of class 1 are relatively stable.
2. Compounds.
Nitro-glycerine and gun-cotton and their derivatives.
These are chemical compounds, formed by the substitution, in
an organic substance of the general form C^ Hy 0„ of
3 molecules of NO2 for 3 atoms of H.
The weak affinity of N renders the NO^ a readily acces-
sible magazine of oxygen.
Explosives of class 2 are called high explosives, and
are relatively unstable. In this class are included the
fulminatmg compounds. See Chap. XIV.
GUNPOWDER.
This is formed of a mixture of KNO3; C, and S, in the
proportions of about 75, 15, 10. These proportions are
considerably varied in pyrotechnic compositions.
The conversion of gunpowder is approximately expressed
by the following reaction:
4KN03-|-Q + S=K2C03 + K2S04 + N,-i-2COa4-CO.
The reaction is really much more complex, and varies
with the circumstances attending the explosion, even
though great care be taken to make them constant.
Illustration.
The parts played by the three ingredients may be im-
agined by reference to the forced combustion of coal in a
furnace.
The charcoal, in which form C is introduced, forms the
main supply of fuel. The sulphur, owing to the ease with
which it is ignited, takes the place of the kindling material.
The nitre acts as a bellows forcing in air.
The sulphur also gives coherence to the grain, correct-
ing the friability of a binary mixture of carbon and nitre.
11. — EXPLOSIVE AGENTS. 11
Advantages and Disadvantages.
The facility with which, by varying the proportions and
the arrangement of the ingredients of gunpowder its
conversion may be controlled, and also its comparative
stability against accidental ignition, have hitherto com-
pensated for its defects.
These refer to its bulk, the care required in storage, its
sensitiveness to dampness, the large solid residue left from
its conversion, and the danger attending its manufacture.
While for special purposes, where great force is required, it
is being supplanted by the high explosives; its value, as a
reservoir of potential energy for purposes of propulsion,
increases as our knowledge of its properties extends.
Note to page 7.
1. From the chemistry we have p v =/o ^^o ( 1 H 7 = — 7 ) . If in
\ 273 ^Tdl
this we make v = l, then by definition /= p = — — ^ — - = — .
•^ ^ 273 273 C
III. — INGREDIENTS OF GUNPOWDER.
CHAPTER III.
INGREDIENTS OF GUNPOWDER.
COMBUSTIBLES.
1. Sulphur*
Preparation.
This is refined by distillation. The product is called
"flowers of sulphur," or "rock sulphur " or "brimstone,"
according to the temperature at which the volatile pro-
ducts are condensed.
Properties.
If below 115°, minute crystals or "flowers" are formed;
above that temperature, the vapors condense in a liquid
form, which is cast into moulds. Flowers of sulphur are
not used for gunpowder, as they contain SOg and HgSOji
which are hygroscopic.
2. Charcoal,
Material.
Charcoal used for gunpowder is made from wood, the
composition of which, excluding water and ash, is repre-
sented by CeHioOg, corresponding to the following propor-
tions per cent.:
c,
44
H,
6
0.
50
100
The object of carbonizing the wood is twofold. 1st. To
increase the calorific value of the fuel by increasing the
III. — INGREDIENTS OF GUNPOWDER.
proportion of carbon. 2d. To increase its calorific inten-
sity by facilitating its reduction to powder.
Composition.
Gunpowder charcoal consists of from 55 to 85 per cent,
of carbon with varying proportions of hydrogen, oxygen,
and ash. Its imperfect distillation leaves varying amounts of
hydro-carbons which increase its inflammabiUty, and, owing to
the calorific value of hydrogen, may increase its potential.
Condition.
The uniform action of fired gunpowder and the safety of
its manufacture depend largely upon uniformity in the
condition of the principal fuel which it contains.
Uniformity is sought by using the same kind of wood,
carbonized by the same process; the temperature being
raised at the same rate to a point which, for each grade of
charcoal, is the same.
PREPARATION.
Preliminaries.
White woods, such as the young willow or alder, which
are soft and of rapid growth, are preferably employed,
since they yield a charcoal that is inflammable, friable, and
free from ash.
The bark is removed, so as to facilitate drying in the
open air, and to free the coal from earthy matter and
salts.
Distillation.
The wood is usually distilled in iron retorts, surrounded
by flame consisting largely of the gases evolved by the
process: Figures 1 and 2.
For convenience, the wood is charged in slips^ which are
cylinders of thin sheet iron.
The progress of the operation is judged of by test sticks,
withdrawn from time to time for examination; by the use of
HI. — INGREDIENTS OF GUNPOWDER.
a pyrometer, or by the appearance of the flame and smoke
as follows.
Phenomena of Carbonization.
The rate of distillation being always slow, the character-
istics of the product depend principally upon the temper-
ature at which the process ceases. Five stages are recog-
nized, of which three correspond to useful grades of
charcoal.
I. Up to 150°, desiccation occurs.
II. At 150°, decomposition begins, and continues as fol-
lows: —
1st. H and O are evolved and unite.
2nd. Three acid oxides (carbonic, acetic, and
pyroligneous acids. — COg; CH3, CO2H; CgH^Og)
and an empyreumatic oil of an analogous com-
position are evolved.
3rd. Soot comes forth in heavy clouds.
4th. The gases burn with a ruddy flame.
6th. As the proportion of O diminishes, CO re-
places CO2, and at 260°, the flame becomes blue.
The solid products are called brands (Fr. fumer-
ons)j which smoke in burning.
III. From 260° to 270°, brown charcoal is formed. It is
smokeless but tough.
IV. From 270° to 340° is the period of the formation of
hydro-carbons; both gaseous, viz.: defiant and marsh gases
(Cg H^; C HJ, and in various liquid forms, including coal
tar. The gases burn with a yellow flame, which, as the
proportion of C diminishes, gradually becomes pale.
At 280° the liberation of the hydro-carbons changes the
charcoal from brown to red (charbon roux); it tends to
raise the temperature suddenly to about 340°.
III. — INGREDIENTS OF GUNPOWDER.
The effect of this rise in temperature is to convert the
red coal to the next grade, which is black. The redness
of the product will, therefore, depend upon the care taken
in regulating the temperature. This is done by drawing
the fire, and completing the process by the residual heat.
The operation is difficult and the product not uniform.
V. Above 340°, black charcoal is formed in proportions
increasing with the temperature, as indicated by the in-
creasing whiteness of the flame.
The effect of increasing the temperature upon the pro-
portions of the constituent elements is shown roughly by
the following table:
Max. Temperature.. 150° 260° 280° 350°
Prr»rln/^fo Dried Brown Red Black
jrruUUCLb. , Wood, Coal. Coal. Coal.
Carbon 44.0 68.0 71.0 77.0
Hydrogen 6.0 5.0 4.5 4.0
Oxygen 50.0 27.0 24.5 19.0
Proportion of Weight
of Dried Wood... 100.0 60 37 30
Physical Properties.
The physical properties also change. The higher the
temperature —
the more — the less —
1. brittle; 1. hygroscopic;
2. hard and dense ; 2. violent as an ingredient
3. prone to spontaneous com- of gunpowder —
bustion —
does charcoal become.
SPONTANEOUS IGNITION OF CHARCOAL,
Cause.
The property of charcoal by which it condenses gases
within its pores, particularly the vapor of water, may raise
its temperature to the point of ignition. This ^ facilitated
in. — INGREDIENTS OF GUNPOWDER.
by the occluded oxygen and by the increased surface result-
ing from pulverization.
Preservation.
To prevent accident, it is cooled slowly, and kept in the
stick for several days. To obtain uniformity in the amount
of water occluded, it is prepared only as required for use.
Its power of spontaneous ignition, when pulverized, is
destroyed by mixing it with sulphur or nitre.
MANUFACTURE OF BROWN CHARCOAL BY SUPERHEATED
STEAM.
Process.
The uniform production of brown charcoal may be
accomplished by exposing it for a longer period to a some-
what lower temperature than that above assigned as the
maximum. For this purpose superheated steam is used, as
shown in figure 3.
Eetort.
The retort is a fixed vertical cylinder of boiler iron,
jacketed with mineral cotton. (Bloxam, Art. 217.)
Through perforations in the cast-iron top enters a cur-
rent of steam which has been superheated in a coil to about
230°.
The wood is piled vertically on a perforated false bottom
made fast to an axial bar, by which the contents can be
removed.
The condensed steam and the water, acids, and tar drain
through the pipe shown.
Product.
The process lasts about four hours, being stopped when
experience shows that the fibrous structure of the wood is
about to disappear.
The fiber, which is retained for its binding effect on the
structure of the powder made from this coal, notably
increases the difficulty of pulverizing it.
III. — INGREDIENTS OF GUNPOWDER.
OXYDIZING AGENTS.
1. Nitre.
Source.
Only about one-tenth of the supply of nitre is the native
Indian product; the remainder comes from the double
decomposition of the sodium nitrate with a potassium salt.
Impurities.
The principal impurities are the chlorides, the affinity of
which for moisture renders them objectionable. Not over
■g-g^ is allowed in nitre used for government gunpowder.
2. Sodium Nitrate,
Advantages.
1. It is cheaper than nitre for equal weights.
2. Owing to the relative atomic weights of sodium (23),
and potassium (39), 85 per cent, of the. usual proportion of
nitre suffices as a supply of oxygen, still further reducing
its cost.
3. If the usual proportion of 75 per cent, be retained, the
greater volume of gas evolved increases the force of the
powder and adapts it especially for blasting.
Disadvantages.
1. The deliquescent properties attributed to the salt are
detrimental when the powder made from it is to be stored.
2. The salt is more soluble than nitre, and, therefore,
powder made from it suffers more than ordinary powder
from the segregation of the salt by efflorescence. This is
due to the acqueous vapor condensed in the pores of the
charcoal which the powder contains. When the powder is
made on the spot where it is used, as in the excavation of the
Suez Canal, this objection need not apply.
III. INGREDIENTS OF GUNPOWDER.
3. Potassium Chlorate.
Disadvantages.
1. The low temperature of conversion, due to the affinity
of chlorine for the metals, renders the powder dangerous
when exposed to shock.
2. Its conversion gives free chlorine, which attacks the
bore of the gun and is injurious to the gunners.
3. It is costly.
4. The uncontrollable violence of mixtures containing
the chlorates relegates them to the category of the high
explosives discussed in Chap. XIV.
They are principally iemployed for igniting other explo*
5ives; themselves being ignited by friction.
4. Ammonium Nitrate,
This is becoming extensively used in the so-called smoke-
less powders for heavy cannon.
Advantages.
The products of combustion are gaseous or volatile, so
that the smoke is greatly diminished in density, and the
entire volume occupied by the powder is available for the
expansion of the gases.
Disadvantages.
The deliquescence of this salt requires that powder made
from it be hermetically sealed. This prevents the use of
the ordinary cartridge bags.
IV. THE MANUFACTURE OF GUNPOWDER.
CHAPTER IV.
THE MANUFACTURE OF GUNPOWDER.
ACCIDENTS.
Buildings.
Owing to the danger of explosion the buildings are scat-
tered as much as possible and are separated by traverses or
rows of trees. Figs. 1, 2.
The buildings are generally constructed with heavy walls
on three sides, the remaining side and the roof being as
light as practicable, so as not to increase the violence of
explosions by unnecessary confinement. Fig. 3.
Power.
The machines employed are usually automatic, power being
conveyed by canals (fig. 1), or wire rope (fig. 2), radiating
from a central steam engine. As a general rule safety is
enhanced by slowly operating the machines.
Precautions.
The machines are started and stopped from an outside
shelter, the completion of the operation being indicated by
an automatic signal. Great care is taken to prevent the in-
troduction of foreign matter, the workmen being required
to change their clothing before entering, and wearing rubber
overshoes within the buildings, at the door of each of which
is a wet mat.
All parts of the machines liable to become loose are boxed
in. Iron is replaced, wherever possible, by gun-metal, copper,
or wood.
IV. — THE MANUFACTURE OP GUNPOWDER.
Automatic devices are arranged to drench the contents of
buildings adjacent to a probable explosion.
The diffusion of dust is avoided by boxing in those
machines which produce it.
Powder in barrels is always gently handled. It should
never be rolled for transportation.
These details are given to suggest the precautions neces-
sary while handling gunpowder in service.
PRINCIPLES OF THE MACHINES EMPLOYED IN THE MANU-
FACTURE OF GUNPOWDER.
Types.
In order to derive the benefits of continuous operation,
the tools yOX portions of the machines in contact with the
material, are preferably of the rotary type. Reciprocating
motion is objectionable, in that it wastes energy in revers-
ing the direction of the motion at each end of the stroke.
Classification. — The tools employed may be classified ac-
cording to their functions, as follows:
FUNCTIONS.
NAME OP TOOLS.
Nature
of
Operation.
General.
Special.
General. Special.
U.B011S \l^
continuous.
fl. disintegration
intermittent.
{ 2. Barrels tumblins
contnmous.
1.
To divide by
.
fl. cylindrical
continuous.
1 2. separation
Sieves ■
2. flat
1
intermittent by
reciprocating
motion.
fl. mixinff
Batrels tumbling
continuous.
n.
To combine by-j
L2. pressure
fl. rolling
Th'^sjifin \ 2- thrusting
Pi esses \ (hydraulic)
continuous,
intermittent by
reciprocating
motion.
ni.
To convey by
Bands endless
continuous.
The rotary tools may be classified as to whether the
material lies without or within the tool; as —
1st. Rolls.
2d. Tumbling or rolling barrels.
IV. — TME MANU^ACTtrkE OF CtJNfOWDEft.
Rolls.
The object of a roller or roll is twofold.
1st. To concentrate a given pressure on a small area of
contact.
2nd. To transfer this pressure to successive areas contin-
uously.
Relative motion between the material and the tool is, there-
fore, necessary.
Eeduction of Area.
The reduction of area desired is generally attained by
the curvature given to the smooth cylindrical surface of the
roll; it may be increased by fluting the surface or by provid-
ing it with pyramidal points.
The effect upon a granular material then resembles crack-
ing, rather than the crushing effect of the smooth roller.
Transfer of Pressure.
When the pressure is transferred but slowly, the parti-
cles of the material may have time to adjust themselves in
their new positions. The effect of the pressure will then be
rather to condense the material than to disintegrate it by
crushing.
Eelative Motion.
1. When the material is at rest, a single roller is used.
Example: a rolling-pin. See fig. 8.
In practice, the path of the roller is circular, so that its
effects may be repeated.
2. When the material moves, the rollers are in pairs and
revolve on fixed axes in relatively opposite directions. Ex-
ample: A clothes wringer. See fig. 14.
In this case, they act but once upon the material, which is
carried through them by friction, and fed to and removed
from the rollers by its weight.
To assist in feeding automatically, several pairs of rollers
may be placed in tiers, surmounted by a hopper containing
4 IV. — The manufacture op gunpowder.
the material to be disintegrated. The upper tiers have the
coarsest teeth and are placed farthest apart.
A coffee-mill is a variety of this class. The rolls are ver-
tical, concentric, and conical; the outer roll, which is fixed,
being the more obtuse. The funnel-shaped space between
them serves as a hopper, and as the material descends, pro-
duces the effect obtained by the successive tiers above de-
scribed.
Fig. 4 shows a charcoal-mill and sieve. The roll is bal-
anced to avoid excessive pressure.
Barrels,
Type.
Tumbling barrels, as represented in fig. 5, are much used
in the arts for abrasion. Their utility depends upon the
inter-attrition of the contents. In powder making, besides
the material, these often consist of balls, b, b, lifted by ledges,
Z, Z, and continually falling back upon the material beneath
them.
When the operation has proceeded far enough, the door
JD is removed, disclosing a perforated screen through which
the finer portions may gradually escape upon the oscillating
sieve, S.
The product is collected in the drawer Z>/
Varieties.
The nature of the barrel and of the balls varies with the
explosiveness of the material and the character of the
operation. Thus, the barrel may be of iron with iron balls
where an inexplosive material is to be pulverized*; of a
wooden skeleton covered with leather, using bronze or zinc
balls, when the operation is dangerous; or covered with wire
*When the material to be disintegrated is very tough, heavy iron
cylinders are used instead of balls.
IV. — THE MANUFACTURE OF GUNPOWDER.
gauze netting, and using wooden balls, where simple com-
minution of a friable material is desired.
By omitting the balls and varying the size of the netting,
such barrels may be used as sieves; and, by slightly inclining
their axes to the horizon, both ends may be left open, when
they will remove the dust. Fig. 4.
If the barrels be tight and no balls be used, the contents
will be merely polished. Such tools are much used in the
arts for finishing the surface of rough metallic objects, and,
in the manufacture of gunpowder, for glazing it.
Mixing Barrels.
Where simple mixture of the ingredients 'is sought, the
barrel may contain paddles revolving independently upon
its axle, as in a churn, fig. 6. The action of these paddles
is also disintegrating, and, where time is important, may
replace the more crude pulverizing apparatus described.
Advantages.
The principal advantage of the rolling barrels consists in
their cheapness of construction and operation, by which
their number may be multiplied, and the eifects of an
explosion diminished.
Carrying Bands.
These are endless belts of a suitable width, which serve
to carry continuously the material from one part of a
machine to another.
If horizontal, a plain band will suffice; but, if inclined, it
is furnished with elevator buckets. Fig. 7.
OPERATIONS OF MANUFACTURE.
Processes,
Nature.
All the stages of manufacture may be referred to the
following essential processes.
b IV. — THE MANUFACTURE OF GUNPOWDER.
1. Formation of a homogeneous press cake of required
density.
2. Breaking up the press cake into grains of required
size and form.
3. Finishing the grains so formed.
Operations.
The necessary operations may be divided into four
principal groups, viz.:
Jl. Pulverizing.
2. Mixing.
3. Moistening.
II. Operations relating to press cake. ] \ p"ressi^n°^^^^"^'
III. Operations relating to graining, -j \; gjf^/^^"^
IV. Operations relating to finishing.
'1. Glazing.
2. Drying.
3. Dusting.
4. Blending.
5. Marking.
X PRELIMINARY OPERATIONS.
1. Pulverizing,
Process.
The nitre is generally in crystals that are sufficiently
fine. Otherwise, this and the other materials are pulverized
by any suitable process, either separately under single rolls
or by a binary process in a barrel, viz.: the charcoal and
sulphur together, or the charcoal and nitre together.
Object.
The pulverization should be thorough, so as to reduce
the time required for incorporation ; the latter, owing to the
cost of the plant and the smallness of the " charges " treated,
is the most expensive of the operations.
IV. — THE MANUFACTURE OF GUNPOWDER. 7
2. Mixiftg.
The three ingredients may be mixed by hand or in the
rolling barrel.
3. Moistening.
Object.
The object of moistening is generally to assist in the
distribution of the nitre; to give consistency to the mass;
and to prevent a dangerous rise in temperature during the
various operations of manufacture.
Limits.
An excess of moisture may cause segregation of the
nitre by crystallization, and its evaporation, as in store, may
render the finished powder unduly porous.
On the other hand, extreme desiccation may lead to the
re-absorption of hygrometric moisture, which would affect
the properties of the powder dried.
The amount of moisture should never exceed 3 or 4 per
cent. It is frequently renewed during manufacture, accord-
ing to the state of the atmosphere and to the special object
in view. The amount present is determined by desiccating
a weighed sample.
II. OPERATIONS RELATING TO PRESS CAKE.
1. Incorporating.
Object.
This is intended to unite the dust of the ingredients as
intimately as mechanical means permit, and thereby to facili-
tate the conversion of the powder into gas. It is the most
important of all the operations of manufacture.
Process.
The wheel mill (Figs. 8 and 9), used for this purpose, con-
sists of two cast-iron cylinders Cy c^ weighing several tons
each and acting as single rolls.
b IV. — THE MANUFACTURE OF GUNPOWDER.
In order that their effect may be exerted throughout the
layer of composition, this is made only about one inch thick.
The risk attending this disposition is diminished by fre-
quent careful moistening, and by the eccentricity of the axle;
this permits the wheels to rise and fall as obstacles are
encountered. The constancy of the resulting pressure in-
creases the uniformity of their effect. This arrangement is
shown in Fig. 9.
The arrangement of the wheels upon an axis rotating in
a horizontal plane peculiarly adapts them to the require-
ments of this operation. For, while both edges of either
wheel have the same angular velocity, their paths described
in the same time are notably different. Hence, it follows
that the inner ed^e will tend to slide backward relatively to
the outer edge; giving to the wheel a motion of rotation
about an instantaneous vertical axis, combined with that
about its permanent horizontal axis.
The effect is to grind the material nearest to the centre
more thoroughly than that nearest to the curb of the
trough; because in the former case, the sliding of the wheel
repeats the effect of its crushing, and, in the latter case
replaces it in part.
This effect is distributed by means of ploughs preceding
the wheels, and by causing the wheels to travel in different
paths.
The process takes about two hours, depending on the
quality of the product; it continues day and night, while
that of the other machines is confined to daylight.
Product.
The product of the wheel mill, called mi7/ cake, unless
consolidated by very slow rolling, is friable and of variable
thickness and density. These defects are corrected by the
next process.
The perfectness of the incorporation may be tested by
IV. — THE MANUFACTURE OF GUNPOWDER. 9
flashing a small quantity upon a glass plate. No residue
should be left. The stains left by flashing powder on the
blue paper used in solar printing are characteristic, and
increase the delicacy of the test.
Variations in Process.
In case of necessity the incorporation may be less
perfectly performed by the stamp mill (Fig. 13), or by the
protracted use of the rolling barrel. (See also page 15.)
2. Pressing,
Object.
The object of pressing powder is to increase its density
as a fuel, and to give it sufficient hardness to resist the
formation of dust in transportation.
Kind of Press.
The intensity and uniformity of the pressure required
usually demand the action of an hydraulic press, Fig. 10;
although, when quantity rather than quality is desired,
single or double rolls may be employed.
Process.
To increase the uniformity of the material pressed, the
product of the various wheel mills is coarsely granulated
and mixed. Then, having been moistened, it is placed in
layers between plates which are kept at about two inches
apart until the spaces between them are filled.
The powder is then gradually compressed to about half
its former volume; being kept from spreading by hinged
side pieces, which, being latched together, form a sort of
box. This box is generally vertical, but for convenience is^
preferably horizontal and on the level of the floor.
Variations in Density.
The resulting density increases within limits, with the
duration of the pressure and with the amount of trituration
which the powder has received. The proportion of mois-
10 IV. — THE MANUFACTURE OF GUNPOWDER.
ture largely affects the density, since it acts as a lubricant
between the particles. The density is not uniform through-
out the press cake, being always greatest next to the mov-
ing surface.
To obtain uniform density, upon which it will be seen
that the uniform action of powder greatly depends, one
must compress equal masses equally incorporated and con-
taining equal quantities of water at equal rates into equal
volumes.
Wiener's Powder.
These requisites are with difficulty attained, owing to the
variable hygrometric condition of the atmosphere. It has
been attempted to dispense with water for pressing, by
heating the powder during this operation slightly above the
melting point of sulphur.
This process, invented by Colonel Wiener, of Russia,
renders the gunpowder practically waterproof.
Effect of Form of Plates.
The plates between which the powder is pressed are gen-
erally flat, in which case the press cake comes from the press
in slate-like slabs. The powder, resulting from breaking up
these cakes, is called of irregular granulation^ or simply
grained powder.
Modern powders for heavy guns are often pressed be-
tween plates, the surfaces of which are regularly indented
or ribbed after the manner of a waffle iron (Figs. 11, 12).
The resulting press cake may be readily broken up into
grains of great uniformity of size and shape. Such powders
are said to be of regular granulation.
Molded Powder.
When the press cake is made exceedingly small, so that
each cake shall make one grain, the powder is said to be
molded. See molded J>rismatic, Figure 12.
IV. — THE MANUFACTURE OF GUNPOWDER. 11
Such powders are made by a number of properly shaped
punches and dies simultaneously operated. Fig. 15, post.
Concrete Powders.
The structural homogeneity of the product depends
much upon the condition of the material compressed. If
the soft mill cake, above referred to, be replaced by that
which has already been pressed and granulated, a co7icrete
powder is produced; the fine grains composing it being
cemented together by the pressure into a mass, the
porosity of which is greatest in the middle. The burning
of this powder is notably different from that of the homo-
geneous mass generally produced.
OPERATIONS RELATING TO GRAINING.
Object.
The object of graining, like that of splitting fire wood, is
to increase the initial surface of combustion.
Operations.
The press cake is broken up by a series of rolls (Fig. 14),
and sifted between limiting sieves.
Principle of Gauging.
The use of these sieves illustrates a principle common in
manufactures; this principle when it is applied tp individual
articles, is called gauging.
Assuming that no two objects can be made of precisely
the same size, a certain tolerance is established by the
adoption of a maximum gauge, through which each object
must pass, and of a minimum gauge, through which no ob-
ject may pass.
The grains which are too coarse or too fine are reworked.
Special Operations in Graining,
Regular Granulation.
These depend upon the kind of grain required. For
13 IV. — THE MANUFACTURE OF GUNPOWDER.
example, the powders of regular granulation require only
breaking up as by hand.
Pebble Powder.
The English cubical, or pebble powder is made by cutting
the flat press cake into prisms between ribbed rolls, and
then recutting these prisms across their length.
Flat Powder.
The flat French powder (Castan's) is made by roughly
breaking a rather thin press cake, so as to make the thick-
ness of the cake the minimum dimension of the finished
grain. (Fi^. 12.)
IV. — OPERATIONS RELATING TO FINISHING,
1. Glazing,
Object.
The object of glazing is to remove the angles and asper-
ities of the grain; these would form dust in transportation
and facilitate the absorption of moisture in store.
It compensates for the diminished density of the interior
of the press cake from which most of the grains are formed,
by increasing their superficial density by their mutual col-
lision; it also increases the homogeneity of their struc-
ture by the heat which is thus evolved.
Process.
Moisture having been added to give some plasticity, the
grains are rolled in a wooden barrel without balls.
2. Drying,
Object.
The object of drying is to reduce to normal limits, the
moisture required in the previous stages of manufacture.
Process.
It is accomplished by passing a current of warm, dry air
through successive layers'of powder spread on screens or
on shallow trays.
IV. — THE MANUFACTURE OF GUNPOWDER. 13
The temperature should be increased gradually, to avoid
disintegration of the grains.
3. Dustiftg,
Object.
This is intended to remove the dust resulting from the
glazing, and detached from the surface of the grains by
drying.
4. Blending,
Object.
To neutralize unavoidable variations in manufacture,
powders of the same size and nature may be blended so as
to give certain average results.
Process.
Fine grain powders are mixed according to their densi-
ties, and those of larger grain, according to their ballistic
properties. Molded powders are blended in charges, grain
by grain alternately.
6. Marking,
In the U. S., powders receive certain conventional fac-
tory marks, of which the first two letters generally relate to
the size and use, and the final letters to recorded variations
in the manufacture, or to the date at which certain lots are
made. Thus, I. K. A. might mean the first lot of I. K.
powder used for field guns; E. V. B. the second lot of
hexagonal powder for sea-coast guns, etc. Similar symbols
are used abroad and are very convenient.
VARIATIONS IN MANUFACTURE.
COCOA POWDER.
History.
The most important improvement in gunpowder, since
1860, is the invention by the Germans of what, from its
color, is called cocoa or brown powder.
14 IV. — THE MANUFACTURE OF GUNPOWDER.
It is notable for being the first important modification of
the long established composition of gunpowder which has
proved practically successful, and, as will be seen, for the
paradoxical nature of its results. In this country it has so
far been used only in heavy cannon.
Characteristics.
As made in this country by the Du Pont Powder Works,
it differs from ordinary powder; —
1. In the composition of the charcoal, which is made by
steam heat, as described Chap. III.
2. In the addition during incorporation of gummy carbo-
hydrates, such as sugar, dextrine, etc.
3. In the proportion of the ingredients —
Nitre, 81.5 per cent.
Charcoal and Carbo-Hydrates, 15.5
Sulphur, 3.
lOOO"
4. It is difficult to ignite, requiring in the gun a few
prisms of black powder to be built into the cartridge near
the mouth of the vent.
6. When ignited, unconfined, it seems to/j/j^^rather than
to deflagrate explosively.
This and its want of friability make it safe to transport
and handle in store.
6. It is quite hygroscopic, but suffers less from moisture
than black powder.
7. Its ballistic properties are extraordinary,
8. It gives comparatively little smoke.
Manufacture.
This resembles that of all the molded concrete powders.
The grams compressed are of the size of mortar powder,
and are slightly moistened before pressing.
TV. — THE MANUFACTURE OF GUNPOWDER. 15
Press for Molded Powders.
Pressing is done by carefully regulating the motion of the
plungers of a duplex hydraulic press, which molds about
100 prisms at a time.
In fig. 15, ^ is a fixed mold plate containing a number of
apertures of a cylindrical or prismatic form, into which the
perforated plungers, G^ Z, fit.
Through the axes of the plungers run needles, H, sim-
ultaneously operated by the toggle-joint, /, and the supple-
mentary cylinder, K.
A quantity of powder is swept into the apertures, X^ until
they, are full. The rams, B^ B' , then approach each other
with equal velocities; and as L enters E, ZT rises into L.
After suitable pressure, L rises; ZT is withdrawn, and G
rises; lifting the prism so that it may be swept off into a
box.
The resulting prism has very dense ends, separated by a
somewhat porous belt.
NORDENFELDT POWDER.
Object.
To increase the intimacy of the incorporation and to
avoid the danger of performing it by mechanical means.
Manufacture.
Charcoal.
Straw or cotton-wool is carbonized by exposure to a
stream of gaseous HCl.
Sulphur.
Dissolved in CS^ and added to Charcoal.
Nitre.
In aqueous solution is gradually added to above.
The mass is mixed by paddles while in a liquid state,
after which the vehicles are distilled and evaporated. The
usual operations following incorporation are then pursued.
V. — INTERIOR BALLISTICS.
CHAPTER V.
INTERIOR BALLISTICS.
Division of Ballistics.
Ballistics, which treats of the motion of projectiles, is
divided into interior and exterior ballistics, according as
the motion of the projectile within or without the gun is
considered.
Interior Ballistics.
The latter science is studied later in the course; but the
former is so intimately related to the conversion of gun-
powder into gas, that it is expedient to deal with it while
the circumstances of this conversion are fresh in our minds.
The Gun as a Machine.
Functionally speaking, the gun is a machine by which the
potential energy of the gunpowder is converted into the
kinetic energy of the projectile.
It is well to consider in advance certain elementary prin-
ciples relating to the construction of this machine and to
the measurement of the energies received and usefully
converted.
FORM OF GUN.
strength vs. Weight of Guns.
It will hereafter appear that,
considering a gun to be com-
posed of a series of elementary
concentric cylinders, the resist-
ance which each of these cylin-
ders offers to a permanent tan-
gential deformation varies in-
versely with the square of its
radius; or, if S represent the
stress, ABy on the interior cir-
tJ^IVE
"\
O^'
.-f*\
V. — INTERIOR BALLISTICS.
cumference of an elementary area of cross section of the
bore, the radius of which is r j and y be the stress from the
same cause at any other radius, x; then j* = — ^ . This is ex-
00
pressed by figure 1.
But the weight of the elementary longitudinal cylinders
increases with the square of their radii.
It therefore appears, that after a certain point, an increase
in the thickness of the walls of the gun adds rapidly to its
weight and but slowly to its strength.
Strength vs. Cost.
Also, when the diameters of cannon exceed a certain
limit, the difficulties of construction attending an increase
in diameter, increase much more rapidly than do those at-
tending an increase in length.
Conclusion as to Form of Gun.
A given amount of energy may, therefore, be most
economically transferred from the gunpowder to the pro-
jectile, by diminishing the rate of transfer and increasing
its duration.
Considerations relating to the weight and cost of a given
cannon having thus determined the most suitable diameter,
it should be kept constant for the entire length of the gun,
provided that the stress to which it is exposed shall also be
constant.
It is the object of recent improvements in guns, powder,
and projectiles, to make this stress as high as it is safe, and
to prolong it as far as possible throughout the length of the
bore.
Recent changes in the profile of cannon illustrate the
progress which has so far been attained toward realizing the
conditions of this ideal gun.
-INTERIOR BALLISTICS.
FORM OF PROJECTILE.
Until quite recently, all but experimental cannon were
muzzle loaders.
Until about 1860, they were smooth-bores and fired
spherical balls.
The success of the rifled field pieces in the war between
France and Austria led to the general use of projectiles,
oblong in shape, but, like the spherical projectiles, smaller
than the bore.
These cannon have been recently replaced by rifled
breech loaders, firing projectiles provided with a compres-
sible ring slightly greater in diameter than the bore.
The enlarged chamber, which this form of projectile re-
quires, and the resistance which it offers to motion, consid-
erably modify the circumstances of the conversion.
Note. — This chapter is introductory to the seven following chapters.
VI. — VELOCIMETERS.
CHAPTER VI.
VELOCIMETERS.
Object. — In order to study experimentally the transfor-
mation of energy from the gunpowder to the projectile and
to the gun and carriage, and to measure the kinetic energy
residing in the projectile, both as it leaves the gun and when
it has done work upon the medium through which it passes,
special instruments, known as velocimeters^ chronographs^
chronoscopes, etc., have been devised.
Importance. — Except where otherwise specified, the fol-
lowing discussion relates to the means employed for meas-
uring the initial velocity of the projectile. This is the great
measure upon which all ballistic predictions are based.
Constituent Parts. — All such instruments are chronometers
and consist essentially of a register and a marker.
The register has a known velocity relative to that of the
marker and receives from it a succession of marks, the
time equivalents of the spaces between which measure the
periods between certain events.
The events are the first visible effects produced upon the
velocimeter by the arrival of the projectile at certain
epochal points. These are often targets.
Signal Time. — The interval between an epoch and the
corresponding event is called the time of transmission, or
the signal time. See figure 14.
The time from any origin to an event = time to the
epoch, /, + signal time, G\ and the interval between two
events, 8 =(/" + a") - {t' + 6')^{t" -f) + (a' - c'). If
G''-a'=Oj t'-t', or r, =d. If a"-a'=Cj r=d-C; if
•then r=0, d--C. To diminish accidental variations in C,
a is made as small as possible. Knowing s, the distance
between the epochal points, and r, the mean velocity of the
projectile over the intervening path may be determined.
VI. VELOCIMETERS.
Functions of Velocimeters. — Conceiving times and dis-
tances as being each measured from common origins, we
may say that the instruments record differences in instru-
mental distance corresponding to differences in time,
which differences in time correspond to differences in dis-
tance of the projectile from any point upon its trajectory.
Classification. — The velocimeters may be divided into
three general classes according as they are adapted to
record: —
I. One difference in time corresponding to one definite
difference of distance of the projectile from a common
origin.
II. Successive differences in time corresponding to sev-
eral successive definite differences of distance of the pro-
jectile from a common origin.
III. Continuous differences in time corresponding to con-
tinuous differences of distance of the projectile from a com-
mon origin.
Comparison of Classes. — For each fire the instruments of
class I determine the mean velocity of the projectile between
one pair of points.
Those of class II determine that between several succes-
sive pairs of points.
Those of class III set forth continuously the circumstances
of the motion.
By taking the epochal points at constant intervals, either
of distance or of time, the indications of the instruments of
class II may, by interpolation, serve to determine the varia-
tions in velocity corresponding to known values of A J or A r
and thus to approximate to the law of motion more fully
expressed by the record of instruments of class III.
This method enables the epochal points to be separated
further than the construction of the instruments of class III
permits.
VI. — VELOCIMETERS.
CLASS I.
Events.— In class I the events are those of the falling of
certain masses, either freely or with constrained motion.
The position of the marks indicates indirectly the interval
of time separating the events.
Operation. — Calling the masses respectively a and b, ac-
cording to their priority of fall, b is caused to strike a while
a is falling. The problem resolves itself into determining
the difference between two intervals of time, viz.:
4=how long a was falling before it was struck.
/b=how long it took b to strike a.
Then 4— 4=0=time that a was falling before b started
to strike it=:the interval between the starting of a and of b^
which is the time interval required.
a and b are generally caused to fall by the demagnetiza-
tion of electro-magnets in separate circuits, which are broken
by the arrival of the projectile at the epochal points. Or
they may be made to fall by the cutting of taut threads by
which they have been suspended.
Disjunctor. — An essential appendage to machines of this
class is the disjunctor^ by means of which, both circuits being
simultaneously broken, the masses a and b are caused sim-
ultaneously to fall.
EXAMPLES OF CLASS I.
1. THE BENTON VELOCIMETER.
See figures 1, 2 and 3.
Description.— This instrument, devised by the late Colo-
nel J. G. Benton, the first Instructor of Ordnance and Gun-
nery at the U. S. Military Academy, employs either elec-
tricity or threads to support a and b. These are similar
pendulums suspended at the centre d of the arc b c a so
that they are constrained to oscillate in adjacent planes par-
allel and close to the face of the arc; this arc, being gradu-
ated, forms the register.
VI. VELOCIMETERS.
That pendulum which lies nearest to the arc carries at its
outer end the marker; this is a delicate bent lever pivoting
in a plane perpendicular to the arc, and so placed that its
inner end, which is lightly covered with printing ink, shall
travel close to the register.
As the pendulums pass each other, a projection on tb.e
inner face of the outer pendulum strikes the outer end of
the marker and causes it to indicate the point of meeting as
at c^ figure 2.
Inspection of the figure shows 0=4 — 4=time of passage
over the arc a o c^ minus time of passage over the arc b ^:=2X
time of passage over the arc o c.
Disjunctor. — The disjunctor in this instrument serves to
determine C, the difference in signal times.
It consists of two flat steel blades, mn, ni'n', secured to
the base at m^ 7n' ^ and having their free ends, n^ «', resting
upon posts ^, b'^ through which and the blades the electric
current passes.
Between the blades is a powerful bent spring r, provided
with a cross piece p q, which lies beneath the blades and
lifts them when the spring is released from the latch g. The
button Sy having been pressed, contact is made; it is broken
by pinching the latch.
Determination of Time Value of Record. — To determine
the time corresponding to a given reading, let / be the
length of the equivalent simple pendulum ; v the velocity of
the center of oscillation or point b; y the vertical distance
passed over by this point; x the variable angle which the
axis of the pendulum makes with the vertical; and t' the
time necessary for the point b to pass over an entire circum-
ference, the radius of which is /, with a uniform velocity v.
We then have :
V=:
y/2gy.
VI.— VELOCIMETERS.
Substituting for y its value in terms of x, the above ex-
i:)ression becomes :
^=V2^^"7cos^
from which it is evident that the velocity of the pendulum
increases from its highest to its lowest point.
The time /' is equal to the circumference of the circle,
the radius of which is /, divided by the velocity v; if this
value of f be again divided by 360, we shall have very
nearly the time of passing over any degree at the height y^
or —
2 7tl
t=
360^2^/ cos ^.
Calling /" the time of a single vibration of the pendulum
of the machine, we have by known laws —
Substituting this value in the equation above, and represent-
ing—
jg^|by«, wehave
V COS X.
To determine /", the pendulums are removed from the
machine, and the cylindrical journals about which they re-
volve are replaced by others, the bearing surfaces of which
are knife edges. Each pendulum is started vibrating through
a very small arc. By means of a stop-watch the time of
1,000 vibrations may be found. By repeating the operation
several times and taking the mean, the time of a single
vibration may be determined very exactly. This time for
pendulums of recent construction is 0.378 of a second.
VI. — VfiLOClMETERS.
If now X be made successively equal to 1°, 2°, 3°, &c.,
and the corresponding values of / be found, we shall have
the time of passage of the pendulum over each degree.
By adding the time of passage over the first degree to
that over the second, we shall have the time of passage
over an arc of 2°. In the same manner, by adding this
latter time to that over the third degree, we shall have the
time of passage over an arc of 3°, and so on.
The following table has been determined in this manner:
Table.
De-
grefeB.
Time in seconds
of passage over
each degree.
Sum of times in
seconds.
De-
grees.
Time in seconds
of passage over
each degree.
Sum of times in
seconds.
1
.00148504
.00148504
19
.00152749
.02849909
2
.00148538
.00297042
20
.00153174
.03003083
3
.00148594
.00445636
21
.00153684
.0315676T
4
.00148673
.00594309
22
.00154213
.03310980
5
.00148775
.00743084
23
.00154772
.03465752
6
.00118001
.00891985
24
.00155361
.03621113
7
.00149019
.01041034
25
.00155980
.03777098
8
.00149221
.01190255
26
.00156630
.03933723
9
.00149415
.01339670
27
.00157313
.04091036
10
.00149033
.01489303
28
.00158029
.04249065
11
.00149876
.01639179
29
.00158780
.04407845
12
.00150142
.01789321
30
.00159565
.01567410
13
.00150433
.01939754
31
.00160388
.04727798
14
.00150749
.02090503
32
.00161248
.04889046
15
.00151089
.02241592
33
.00162147
.05051193
16
.00151455
.02393047
34
.00:63087
.05214280
17
.00151847
.02544894
35
.00164070
.05378350
18
.00152266
.02097160
36
.00165092
.05543442
To Compute a Scale of Velocities. — It should be rem.em-
bered that the times above determined correspond to but
half the difference of the arcs described by the two pen-
dulums; therefore, they should be doubled in order to get
the time r.
2. THE LE BOULENGE CHRONOGRAPH.
See Figures 4, 5, 8, 9.
Description. — This velocimeter, invented by Captain Le
Boulenge of the Belgian artillery, is the one used generally
throughout the world for the determination of initial
Vt. — vfiLO^iMETERg.
velocities. In it the masses a and b are rods falling
freely from electro-magnets E, E' . These are supported
on a stand s, so placed that while a may fall through the
foot of the stand, the fall of b is arrested by a trigger /,
the shock upon which releases a knife-shaped marker m.
The edge of this marker lies close to the path of a, so that
a very slight movement of it to the right, under the impulse
of a powerful spring which is liberated by the fall of b^
produces a mark upon that elementary circle of a which
was opposite to 7n at the moment of impact.
Disjunctor. — Although the operation of the disjunctor is
the same as with the Benton velocimeter, its object in the
LeBoulenge instrument is quite different.
It serves, by making r=(9, to determine the value of 4*
since then 4=4> o^^ the time that a was falling before it
was struck measures the time required for b to strike it.
This instrument does not serve to determine the signal
time, but it may be shown that if the difference in signal
times remains constant the time recorded between the
events = time between the epochs, or 0=?.
Operation. — This mark may be made in three ways, as
follows:
1. Release m while a is at rest; the mark will fall at O,
which is the origin for future measurements.
2. By means of the disjunctor, rupture E and E' simul-
taneously; the mark will be at some point Z> at a height h
above O, corresponding to the time required for b to fall to
m and for m to mark the rod a. This time is /,
1 1h
or the time required for b to strike a. The mark D is
called the disjunction mark.
3. Use as Megagraph. — Rupture E and immediately
afterward E'\ the mark will occur, as at R^ at a height /%'
above O. This is the usual case in practice. Then
VI. — VELOCIMETERS.
•v
2 h'
= the time during which a was falling before
i
it was struck, and t^—t^=Q^ as with the Benton velocimeter.
The mark R is called the record mark.
As a matter of convenience only, the construction of the
instrument permits 4 to be made constant =0^ 15, so that
a rule may be so graduated, that, for a given interval be-
tween targets, the velocity corresponding to a height OR
s s
may be obtained by simple inspection, for v =—=
T 4-OM5
The instrument so arranged is called a Megagraph.
(Greek ^eya8,-great.)
Use as Micrograph. — By raising E' so that the lower
end of b may be nearly level with the top of a, D will be
made to occur near that section of a which passes m with
the greatest velocity. This serves to verify the accuracy
of the operation of the disjunctor, of the magnets, and of
the marking apparatus; since, if these parts worked with
perfect uniformity, successive disjunction marks would be
found at the same height above O. The velocity of a at
the moment of marking magnifies the visible consequences
of deficient uniformity and assists in correcting the causes
to which it is due.
With this arrangement, if b is detached before a^ the
mark will be found as at R and Q=t^—t^.
The advantages of this arrangement for the measure-
ment of very small intervals of time give it the name of
micrograph. (Greek fxiupoB^-smali.)
Determination of time limit. — The following reasoning
determines the circumstances under which the instrument
should be used as a megagraph, or as a micrograph.
Considering for the moment 0r=r and remembering that
we are measuring the interval t=- we see that, with the in-
V
VI. — VELOCIMETERS.
strument arranged as a megagraph, r may be greatly dimin-
ished by increasing v and reducing s. The mark R will then
be made near D where a has but little velocity, and therefore
imperceptible differences in h may correspond to considerable
differences in r and hence in v. Since the instrument was
invented, initial velocities have increased from 1,200 f. s. to
over 2,000 f. s. while s may be restricted, as at West Point,
so as to be reduced from 50 metres (164 feet, for which interval
the instrument was made) to but 50 feet and even less.
On the other hand, when using the instrument as a
micrograph, if r increase unduly, the mark will occur in
the same neighborhood as before, and the same conse-
quences will ensue.
It becomes therefore necessary to determine a common
time limit within which the instrument should be used as a
micrograph and beyond which as a megagraph.
For this time the mark will, in both cases, occur at the
same height above O. For the megagraph, it will be at
the height corresponding to 4=r + 0^''*'-.15.
For the micrograph, since the length of ^=about 0.5
metre, the maximum value of /b=:0^®*^-.32; therefore, 4=
Qsec.32_2'.
Equating these two values of 4, we have r=0.^®^085 as
the value of the time limit.
Details of the Instrument.
Chronometer. — Referring to the definitions, p. 1, the
rod a is seen to be a register^ the time of fall of which to
any distance h below the edge of the knife making the
mark (9, is known.
This rod in this instrument is called the chronometer. It
is enclosed by a tightly fitting zinc tube which receives the
marks. By turning this tube axially, and finally by revers-
ing it, many records may be made before it need be changed,
10 VI. — VELOCIMETERS.
Registrar. — The rod b is called the registrar. It is much
lighter than a.
Adjustment. — To diminish differences in the time of de-
magnetization, the power of the magnets, E, E\ is reduced
to a safe minimum, which, by the movable screw-cores con-
tained in the magnets, is determined as follows: —
A definite surplus of power* is assured by attaching to
each armature a make-weight in the form of a tube of -^
the weight of the armature. The weighted armature having
been suspended from the magnet, the core of the latter is
slowly unscrewed until the armature falls. The make-
weight is removed before the armature is again applied.
Disjunction Circle. — When it is desired to read velocities
directly from the rule, the value of t^ is made constant by
varying the height of fall of b so that the mark shall fall
upon a disjunction circle previously traced upon the zinc
recorder at a height above O = ~ — ^ — •
Levelling. — The instrument is levelled by using the sus-
pended chronometer as a plumb,
between the epochs.
Bregers Improvemen'.s. — In order to diminish variations
in o'a— o'b resulting from variations in the method of rupture,
depending upon whether the circuit is broken by the dis-
junctor or by impact of the projectile on the target wires, the
improvements of Captain Breger of the French service
tend: —
1. To diminish differences in the time and velocity of
rupture of the two circuits by the disjunctor, which differ-
ences are due to the unequal operating of the parts of the
disjunctor.
Such differences are found to make material differences
in the times required to demagnetize E, E', in consequence
of variations in the intensity of the induced currents follow-
ing variations in the method of rupture.
VI. — VELOCIMETERS. 11
2. Differences in the rate of demagnetization have been
avoided by making as nearly equal as possible the masses
a and b, and therefore the magnetic states of E and E'.
These and other minor mechanical improvements have
diminished the mean error to ^ of that form.erly found.
CLASS II.
Register. — The register in these instruments generally
consists of a revolving polished metallic cylinder, the angu-
lar velocity of which is known. The surface of the cylinder
is preferably smoked, so as to make visible the marks which
it receives.
Marks. — The marks are made in two general ways; —
1st. By the trace of a quill point held lightly against
the cylinder.
By giving the quill point relative longitudinal motion
during the rotation of the cylinder, the trace may be
greatly developed helically.
This trace being developed during the motion of the
projectile, the latter's arrival at an epochal point may be
signalized by a sudden motion of the quill point along a
rectilinear element of the cylinder, causing a jog or offset
in the trace. See Fig. 6. The offset is here the mark.
This motion may be caused by the action of a spring
previously in equilibrium with the attraction of an electro-
magnet. This magnet is included in a circuit that is broken
by the arrival of the projectile at the epochal point.
If the circuit can be re-established before the next
epochal point is reached by the projectile, the quill point
will return to the prolongation of the trace, and one quill
point will suffice. Otherwise, as in Fig. 6, as many quill
points and circuits are needed as there are epochal points.
3nd. The mark may result from the passage of an
induced electric spark caused by the rupture of a primary
circuit at each epochal point.
13 VI. — VELOCIMETERS.
Signal Times. — In order to avoid variations in the time
of signaling, it is advisable, in both cases above cited, to
include all the epochal points in the same circuit and to
provide each of them with the means of renewing the
broken circuit automatically before the projectile can arrive
at the next point. See Targets, Class II, below.
When the times to be measured are exceedingly minute,
this may not be feasible. Equality in signal times is then
sought by increasing the delicacy of the apparatus and
is verified by the simultaneous rupture of as many circuits
as there are markers to be operated.
Tuning Fork. — Uniformity in the rotation of the cylinder
is either assumed from the accuracy of the apparatus or
may be neglected by attaching a tracing quill to one of the
tines of a tuning fork, the time of vibration of which is
known.
The trace then takes the form of a harmonic curve, the
alternate intersections of which with a median trace, formed
when the fork is at rest, mark the ends of each double
vibration of the fork.
The duration of the double vibration is the unit of
measure of time; if the velocity of the surface upon which
the trace is formed be constant during any double vibration,
fractional parts of the intercepted median line will measure
corresponding portions of the unit of time.
The double vibration, instead of the single vibration, is
selected as the unit in order to neutralize errors of meas-
urement. The median line gives the most definite inter-
sections with the harmonic curve.
Interrupter. — When the total time of the observation re-
quires it, the vibrations of the fork F, Fig. 7, may be sustained
by the use of adjacent electro-magnets, w, w, the attrac-
tion of which separates the tines, /, t, until the rupture of the
circuit through the spring R^ releases them. The spring is
VT. VELOCIMETERS.
13
used instead of a rigid contact so as to prolong the influ-
ence of the magnets. The reaction of the fork due to its
elasticity renews the circuit and makes the process con-
tinuous.
This device, as applied to the Schultz Chronoscope, is
known in this country as the Russell interrupter. It is due
to Captain Russell of the Ordnance Department.
When the total time of vibration is very short, no inter-
rupter is required. In this case the fork may be set vibrat-
ing by the sudden withdrawal of a wedge inserted between
its tines; it is then abandoned.
CLASS III.
In instruments of this class relative motion is given to
the register directly by the motion, either of the piece or
of the projectile.
The velocity of the register at any portion of its path is
determined by tracing upon it a harmonic curve with the
tuning fork, or by giving it a known velocity at right angles
to that of the moving part. In either case, a compound
curve is traced from which the required relations between
space and time may be deduced.
Examples: —
If to a gun about to recoil be fastened a bar upon the
smoked surface of which the harmonic curve is traced dur-
ing the recoil, or if some point of the gun be kept in con-
tact with a cylinder rotating at a known velocity about an
axis parallel to the direction of the recoil, we may in
both cases determine by interpolation the velocities desired:
For example: —
Travel
Time.
A/
A X
ft.
0.00
0.02
0.04
sec.
0.0000000
0.0018182
0.0023772
sec.
0.0018182
0.0005590
f. S.
11.0
35.8
14 VI. — VELOCIMETERS.
Knowing thus the mean velocities between many pairs
of epochal pjints, it is possible by interpolation to deter-
mine the accelerations at each of the epochal points and,
knowing the mass of the moving object, to determine the
intensity of the pressure accelerating it.
TARGETS.
CLASS I.
The epochal points are generally wire screens stretched
across the trajectory, as shown in Fig. 9.
Cannon. — In order to prevent injury to the first screen
and to allow for the acceleration of the projectile for a
short distance after it has left the muzzle, due to the rela-
tively great velocity of the escaping gas, the first screen is
put at a distance from the muzzle, which increases with the
calibre of the gun.
When they are situated in the bore of the gun, as in Cap-
tain Noble's experiments, Figs. 11 and 12, the wire may be
severed by the action of a wedge raised by the passage of
the projectile. This arrangement requires the walls of the
gun to be pierced radially as many times as there are
epochal points.
To avoid this piercing, the L^tard apparatus. Fig. 10, is
devised. It is principally of wood, cemented by resin to
the surface of the bore. The head ot the metaUic bolt, a,
and the metallic washer, b, are held in contact by the cross
pin, c. The impact of the projectile on the point of a breaks
the circuit and sweeps the fragments out to the front.
Small Arms. — For small arms, in order to save the time re-
quired in repairing at each fire the distant target, it consists
of an iron plate having attached to its back a flat elastic
blade, through which the circuit passes as in the disjunctor,
Fig. 3. The shock of impact breaks the circuit which is
immediately re-established by the elasticity of the blade.
VI. — VELOCIMETERS. 15
CLASS II.
Instruments of this class that use but one circuit for all
the targets have an arrangement, shown in Fig. 13.
The weights, IV, depress the free ends of the spring wire
staples, df d, f, so that the current may pass from the brass
plate, ay to the brass plate, <r, through the staple, bj and from
^ to ^ through d, and so on.
When one of the threads / is broken by the projectile,
the free end of one of the tines of d flies upward, break-
ing the circuit for an instant, but renewing it as soon as the
upper side of the oblong hole in c is reached.
The West Point target, figure 15, resembles that above
described, but is applied to instruments of Class I.
A discontinuous copper strip, c, c, c, conveys the current
when the flanged copper tubes /, t (cartridge cases), are drawn
into place by the weights w, w.
When a weight is cut the spring, s, lifts its tube and the
circuit is broken.
Compared with fig. 9, the advantages are —
1. The circuit is broken in the same manner, both by the
disjunctor and by the projectile. See page 10.
2. The tension of the threads and the resistance of the cir-
cuit are more constant than when a spHced, continuous target
wire is used.
3. The targets are more readily mended, and the " short
circuiting " of leading wires by fragments of the target wires
is avoided.
ELECTRIC BATTERIES.
These should be as constant as possible. Where storage
room permits the employment of a large number of elements,
the batteries of the gravity type are preferred, except for pro-
ducing the sparks referred to on page 11.
VII. — PRESSURE GAUGES.
CHAPTER VII.
PRESSURE GAUGES.
Object.
From the circumstances of the case the transfer of energy
from the gunpowder to the projectile is accompanied by a
considerable elastic pressure upon the walls of the gun,
the effects of which, to be guarded against, require the
intensity of the pressure to be known.
History.
Owing to the want of suitable apparatus, pressures were
formerly inferred only from the injury resulting to the gun,
and it was not until the time of Rodman that this important
requisite was supplied. Since then great improvements have
been made, some of which will be described.
Nature of Pressure.
The pressure varies at each instant during the passage of
the projectile through the bore, and is generally taken to be
constant throughout the volume in rear of the projectile at
any point of its path. If we adopt Noble's hypothesis,
hereafter to be explained, this is equivalent to saying that
the gases in rear of the projectile at any instant are of uni-
form density.
But the expansion to the front and rear, in consequence
of the motion of the projectile and of the piece, diminishes
the density of the successive layers, estimated in both direc-
tions from that layer containing the center of gravity of the
system. This layer, called the immovable layer, is practi-
cally taken at the bottom of the bore, where experiment
shows that the maximum pressures occur. See page 17.
VII. — PRESSURE GAUGES.
General Methods Adopted.
Two general methods for measuring the intensity of the
pressure are employed, viz.:
1. Statical.
The statical, in which the elastic pressure is placed in
equilibrio with a known resistance. The objections to this
method relate to the magnitude of the forces to be measured
and to the rapidity with which they vary. It is principally
valuable for determining the intensity of the maximum
pressure at the point at which the measurement is made.
2. Kinetic.
In which the intensity of the pressure at any instant is
deduced from the acceleration given to a known mass.
The objections to this method relate to the minuteness of
the times to be measured and to the consequences of small
. . . A''^
errors m measurmg the spaces, smce a=
By the use of comparatively simple apparatus it permits
the law of the variation in pressure to be approximately
determined.
I.-THE STATIC METHOD.
Rumford's Plan.
In 1792, Count Rumford, who made the first recorded
experiments on powder pressures, sought to measure the
total pressure, P=/ 7t r% of a charge of gunpowder fired in
the closed bore of the eprouvefte, Fig. 1, by determining
the greatest weight, W, that would be lifted by the gas suffi-
ciently to allow the escape of gas to cause an audible report.
Conversely, the weight and the volume being constant, he varied
W
the charge. In either case he assumed P— W oi fiz=. r
But if we represent by /, the time during which the gases
were lifting the tenon of the stopper through the height h^
VII. — PRESSURE GAUGES.
the general expression Mgl = M = P- JV, (whence
/i =
F^W
df
t \ '^^
yf^ ^ J shows that, / being very small, P must have
greatly exceeded W in order that h should have had an
appreciable value.
Process of Deformation.
This, which is the present method, consists —
1st. In determining with a press the tarage^ or law con-
necting known pressures with the observed permanent de-
formations of similar metallic specimens.
2nd. Exposing a similar specimen to the action of powder
gases acting over a known area; observing the resulting
deformation, and inferring from the tarage the intensity of
the total pressure producing the deformation observed.
Methods of Deformation.
The specimen may be deformed in several ways —
1. By making a cut, the length of which increases more
rapidly than its width. Fig. 2.
This is General Rodman's plan.
2. By compressing a cylinder between flat surfaces.
This is Captain Noble's crusher gauge, now generally
employed.
Both methods are adapted for service either within or
without the bore.
Apparatus,
Specimens.
On account of its homogeneity, copper is generally used for
the specimen, although lead, and even silver, are employed.
Pistwi.
The pressures are exerted through a freely moving piston.
When firing, a gas check of some kind prevents the gas from
leaking past the piston.
Gas Checks. — 1. Cup.
The action of this gas check, which illustrates a principle
of frequent application in ordnance, depends upon the
excess of the pressure within the cup over that without it;
VII. — PRESSURE GAUGES.
since any gas that may leak past the edge before it is
fully dilated will expand so readily as to have its density
greatly reduced in comparison with that of the gas within
the cup.
2. Air Packing,
Another form of gas check depends upon a number of
circumferential grooves, surrounding the stem of a closely
fitting piston, Fig. 4. These diminish successively the
tension of any intruding gas and delay its progress, until,
by the departure of the projectile from the gun, the pres-
sure ceases. This principle also is applied in ordnance
construction.
External Housing.
For external use the gauge is contained in a housings
screwed into the walls of the gun and communicating by a
radial hole with the bore. This method is rarely employed
at present. ^
Internal Housing.
For internal service a housing, Fig. 3, contains all the
parts. The drawing represents a Noble internal crusher
gauge, full size.
A is the specimen; B, the cavity; C the body of the
housing, closed by the screw y and the soft metallic gasket K.
I is the piston, the cross section of which is y^^ of a
square inch in area. It is enlarged at E to accommodate
itself to the dilatation of A.
Z> is a cup-shaped copper gas-check acting like a metal-
lic cartridge case, and F is a spring to keep the specimen
in an axial position.
Use of Internal Gauge.
To use the gauge, it is tied to the bottom of the cartridge
so that no powder can pass between it and the bottom of
the bore.
VII. — PRESSURE GAUGES.
It is sometimes recessed into the face of the block of
breech loading guns, so that full charges may be fired. It
has also been similarly recessed into the base of the pro-
jectile.
Advantages of Crusher over Rodman Gauge.
The advantages of the Crusher over the Rodman gauge
are:
1. Size.
The small diameter of the specimen, which enables the
size of the housing to be greatly reduced.
When used internally, the circumstances are therefore
more nearly normal, and, when used externally as in Fig. 13, it
maybe inserted close to the walls of the bore instead of ex-
ternally to the gun as with Rodman's first gauge. Fig. 2.
In the latter case it was found that the gas developed con-
siderable kinetic energy in its passage through the walls
of the gun and struck the pi.ston a blow which vitiated the
results of the experiment. This action accounts for many
anomalies in the early experiments.
When properly used, the fact that the gases act by a
pressure and not by a blow is shown by the sensible persist-
ence of form of a specimen exposed to several similar dis-
charges, and by the experimental verification of calculations
based upon this statical hypothesis.
2. Surface.
The flat face of the piston is less liable to injury and
admits of duplication more easily than does the Rodman
knife.
3. Tarage.
It also admits of giving to the specimen a preliminary
compression before it is exposed to the action of the gas.
This, if nearly equal to that expected within the gun,
diminishes the velocity which the piston can acquire (see
^ost) ; it also serves to verify the tarage.
VII. — PRESSURE GAUGES.
EFFECT OF VARYING THE MASS OF THE PISTON.
Discussion. %
Let /* be the variable gaseous pressure on the piston ; R the
variable resistance to deformation of the specimen; m the
mass of the piston, and v its variable velocity over the
path X.
Let d represent the permanent compression.
Suppose the piston to be in contact with the specimen
and to be indeformable.
We have:
' ^/lPdx-/lRdx. (1)
2
When X is a maximum, v—o\ x^^d, and the equation (1)
becomes
/\pdx=f\Rdx. (2)
Let the curves AFE and BFC in Fig. 5 represent by
their ordinates, respectively, the resistances and pressures
due to successive values of x, and let x represent only
permanent deformation, /. <?., that occurring beyond the
elastic limit of the specimen.
From the nature of powder pressures as hereafter ex-
plained, Chap. XI, the pressure curve will be of the general
form OABC\ and, if OD—d, we have area
OABCDrz^f'^^Pdx,
From the nature of the resistances to deformation, the
curve AFE will present no maximum phase, and the curve
will be of the general form AFE, such that the area
OAEn=^ f^'Rdx.
■/>
Equations 1 and 2 show that the resistance curve, at first
beneath the pressure curve, rises above it when x has some
value = OH,
Vn. — PRESSURE GAUGES.
The statical value of the ordinate E,D^ corresponding to the
maximum compression OD, is determined from the tarage.
The figure shows that, while ED may be greater or less
than IB^ which represents the maximum gaseous pressure,
the difference between these two ordinates will depend
upon the angle at which the curves intersect. If this angle
be such that the difference, P — R, of any two ordinates
corresponding to a common abscissa be relatively small, the
resistance corresponding to the maximum compression may
safely be taken as the maximum gaseous pressure.
But P-R= ^ ^ ,= ma (3)
doc
So that the difference between ED and IB can be
neglected only when the mass of the piston is small and the
initial resistance to deformation is great and increases rapidly.
The last two conditions are satisfied by a preliminary
deformation of the specimen to nearly the total extent that
is expected. Such conditions are represented by figure 6.
The indications of the gauge will be more correct when
the pressure curve approaches parallelism with the axis of
X. It will be seen that this occurs rather with slow-burn-
ing powders, which give a gradual change of pressure, than
with those which act more violently.
Tarage.
The preceding discussion shows that the pressures used
in determining the tarage must be applied so slowly that the
velocity of the piston and of the contiguous parts of the
machine may be neglected. Under such circumstances,
when the specimen is of pure copper, 8 mm. in diameter
and 13 mm. long, the resistance in kilogrammes, T, corres-
ponding to a permanent compression in millimetres, E^ is
given by the following equation.
VII. — PRESSURE GAUGES.
^=551 +531 E,
The tarage would accordingly be represented by a dia-
gram, such as Fig. 7, the initial ordinate being at the elastic
limit, and the co-efficient 531=tan ^, or the reciprocal of
the rate of permanent compression.
V SARRAU'S DEDUCTIONS.
An elaborate deduction by M. Sarrau, shows by an
analysis confirmed by experiment that,^-
Slow Pressure.
I. When the pressure increases slowly, as when the
crusher is used in the chamber of a gun firing ordinary
gunpowder, the maximum pressure is sensibly equal to that
indicated by the tarage.
ftuick Pressure.
II. When the pressure is instantaneously, or very sud-
denly applied, as with some of the high explosives; or
when, with ordinary gunpowder, the crusher is placed in
front of the position occupied by the projectile when at
rest so that the pressure shall be very suddenly applied
when the base of the projectile has passed the mouth of the
hole; then the maximum pressure is sensibly equal to that
corresponding to half the tarage.
The correction increases with the mass of the piston
employed.
THE MANOMETRIC BALANCE.
Object.
This avoids the perturbations due to the mass of the
piston, and permits certain relations between pressures and
time to be determined.
Simple Form.
B, figure 8, is a differential piston, the small end of which
is in contact with the bore, and the large base of which enters
slightly the air-tight cavity C, connected with a manometer
VII. — PRESSURE GAUGES.
tube, M, in which mercury is kept at any given height by
means of air pumped into C.
A slide, a, is held by friction beneath B against the ten-
sion of a spring, r.
The pressure may be determined within limits by finding
at two successive similar fires, the heights of the mercury
permitting and preventing the motion of a.
Compound Form.
Also by providing, say, ten similar pistons of varying
area, moving outwardly from Cj each of them provided,
besides the arrangement ra, with some apparatus such as
described Chap. VI, for recording the intervals of time
corresponding to the motion of the slide a.
II. THE KINETIC METHOD.
This consists in determining the rate of change of the
pressure from the change in rate of motion of some body,
the mass of which is known. This body may be either
I, the projectile; II, the cannon; or III, a piston or auxiliary
projectile, placed in some radial channel communicating
with the bore.
I. THE PROJECTILE.
1. Direct Intermittent Method,
Mayewski's Experiments. Figure 16.
General Mayewski, of Russia, in 1867, attempted to
determine the acceleration of the projectile by attaching to
its base a rod which, passing through the breech of the
gun, ruptured by means of a projection upon it certain
electric currents placed at varying distances from the
initial position of this projection. The conditions of each
fire were made constant, except as to the portion of the
path of the projectile, the duration of which was to be
measured.
10 VII. — PRESSURE GAUGES.
Supposing that x~f[t), he assumed a development
x=At+Bt^-{-Ct^ + nt'' + Qtc., (4)
and determined by trial the values for the co-efficients, A, B^
etc., that would satisfy the instrumental values x and /.
Then,
dx
dt
=A^%Bt-{-ZCt^ + ^nt^^-tio. (5)
d^x
a=-^=2B + %Ct+12nt^ + ttc, (6)
The value of t corresponding to the manimum pressure
d^x
wasfoundby placing— 3 =0, and solving with respect to /;
then, by substitution in equations (1) and (3), the corres-
ponding values of x and a were found.
The intensity per unit of area of the corresponding pres-
sure, is given by the following equation:
d'^x
This pressure is only that giving acceleration to the
projectile. The results, found by adding to B=p n r^ the
pressure found to be required to force the projectile
through the bore, gave reasonably close approximations to
the results of the statical pressure gauges, altiiough the
apparatus was subject to many instrumental errors.
2. Direct Continuous Method,
Sebert's Registering Projectile.
This method, which is applicable only to comparatively
short lengths of bore in guns of large caliber, requires a
hollow cylindrical projectile, such as is shown in Fig. 9. It
VII. — PRESSURE GAUGES. 11
is provided with an axial spindle, S, of rectangular cross
section and rotating freely at each end; one of the sides of
this spindle is covered with a film of soot.
A slide M moves freely on the spindle and bears a
delicate tuning fork 7^ arranged as described, Chap. VI.
When the projectile is fired, the inertia of the slide holds
it relatively at rest while the projectile passes by; the
points of the tines describe such a trace as is shown in
figure 10, in which the parallel straight lines represent the
traces when the slide is slipped along the spindle, the fork
not vibrating.
The effect of the friction between the slide and the
spindle can be shown to be negligible.
Although the path of the slide is limited to less than the
length of the projectile, yet it is within this length of travel
that is generally found the maximum pressure, the rate of
change in reaching which is one of the most important
objects of research.
By placing the slide at the bottom of the spindle, it may
serve to determine the retardation of the projectile in flight;
and, by confining it there by a fragile cross-pin to be broken
on impact, it may determine the varying resistance found in
penetrating a more resisting medium than the air.
3. hidirect Intermittent Method.
Successive Shortening of the Bore.
The mean of the muzzle velocities of a large number of
shots fired under conditions, which, excepting the length of the
bore, were identical, could be laid off as the ordinates of a
curve of which the abscissae should represent the various
paths. The curve would have the form given by Fig. 11.
Calling a the acceleration, we have,
dv dv dx dv /i\
dt dx dt dx
12 VII. — PRESSURE GAUGES.
The figure shows that the subnormal a= corresponding
ordinate v x tan g? = ?; x -r- • (")
^ ax
Therefore, having plotted the curve expressing
v=f(x),
the acceleration at the different points along the bore may
be determined by finding the corresponding values of the
subnormals.
The experiments enabled positive conclusions to be
formed :
1st. As to the smallness of the advantage gained by in-
creasing the length of the bore more than 20 calibers, when
quick powders were used.
2nd. As to the great advantage of progressive powders in
guns of suitable length.
II. THE GUN.
Advantages.
Determining the pressure from the acceleration of the gun
in its recoil affords certain advantages owing: —
1st, To the low velocity of the gun compared to that of
the projectile; this permits a greater number of observations
to be made over a given path.
2d. To the simplicity of the apparatus, which avoids the
mutilation of the piece, and permits it to be used with guns
of varying calibers.
3d. To the aid given in the study of the pressures pre-
vailing at the bottom of the bore.
1. Rodman's Velocimeter ,
Construction.
The original instrument of this description was devised
by General Rodman. It consisted of a cylinder rotating
with a known and uniform velocity about an axis parallel
Vll. — PRESSURE GAUGES. 13
to that of the gun and close to it, A pointer fastened to
the gun traced upon the cylinder during the recoil, a line
which, when developed, gave the successive accelerations of
the recoil. The gun was hung as a pendulum oscillating
in the plane of fire. See figure 17.
Acceleration of Eecoil.
For example, let mm' ^ Fig. 12, be the developed circumfer-
ence traced by the pointer when the projectile is placed at the
muzzle, and the charge uniformly dispersed along the bore ;
and let bb' be the corresponding circumference when the charge
is in place. Then taking axes of space and time, ^S" and T
a = 7 — -ri, as in Chap. VI.
Tlniform Pressure.
The dotted line represents the parabola which would be
traced under the ideal circumstances discussed, Chap. V,
/ V being straight and parallel to t' v' .
Rate of Change of Pressure.
It is evident, from the inclination of the initial portions
of the curve, that ihe velocity is actually acquired much more
rapidly than is desired.
2. Siberfs Velocimeter,
Construction.
The velocimeter of Colonel Sebert of the French service
replaces the rotary cylinder by a broad steel tape, one side
of which is smoked, and against which rest the tines of a
tuning fork set vibrating by the act of recoil. See Chap.
VI.
Velocity of Recoil.
The length of any double vibration measured on the
tape, divided by the time of the double vibration of the
14 Vll.— PRESSURE GAUGES.
fork, gives us the mean velocity of recoil over that portion
of the path selected; from which, calling,
qv =z weight of projectile.
JV = weight of gun.
«/ = weight of powder.
2j = velocity of projectile.
V = velocity of gun.
We have V= -^ (see Chapter VI).
Velocity of Projectile.
Or else, supposing the center of mass of the powder to be
moved to the position occupied by the center of mass of the
gases, which is equivalent to supposing that half the mass of
the powder is added to that of the projectile.
-= --^r (9)
Position of Projectile.
Also, denoting by X the length of recoil at the end of a
time t, and x the corresponding path of the projectile.
Pressure on Base of Projectile.
The method above described permits the construction of
a velocity curve, such as Fig. 11, from which the pressure
corresponding to different positions of the projectile along
the bore may be deduced.
Pressure on Base of Bore.
Also, the difference between two successive velocities, as
determined by the trace of the tuning fork, divided by the
common interval of time, would give the mean accelera-
tion ; this multiplied by the mass of the gun gives the mean
Vn, — PRESSURE GAUGES. 15
total pressure on the bottom of the bore during the same
interval of time.
III. AUXILIARY PROJECTILES EXPELLED THROUGH THE
WALLS OF THE GUN.
1. Bomford's Method.
About 1841, Colonel Bomford, of the Ordnance Depart-
ment, prepared a cannon by boring through its walls a
series of small holes at right angles to its axis, as in Fig. 13,
and placing in each hole a bullet, the velocity of which was
instrumentally determined. The pressure at the various
points, deduced from the velocities communicated to the
balls, determined the form of the old Columbiads.
This method was objectionable, as it treated the powder
pressure as an impulsive force and could not take into
account the varying accelerations of the projectile, as is
done in the following recent inventions.
2. Ricqs Register^ Fig. 14
A cylinder C, revolving with known and uniform velocity,
is enclosed in a box B^ through a groove, Z>, in which slides a
marker F^ in contact with the piston Z.
The weight per unit of the sectional area, ^, of (F-Vl^
may be varied at pleasure.
When the gun is fired, a curve, such as shown, is traced
on the cylindery from which, by finite differences, we have
^= -,. (11)
^= ^(KJf (12)
8. T/ie French Accelerograph,
This projects vertically upward a piston, the mass of
which may be greatly varied by the addition of weights.
16
VIT. — PRESSURE GAUGES.
A fixed tuning fork traces the harmonic curve upon a
blackened surface on the piston.
III. STATIC AND KINETIC METHODS COMBINED,
Objections to Kinetic Method.
It will be seen that the objection to the kinetic method
lies in the liability of error in the measurement of the small
spaces by which the time record is expressed.
This limits the method principally to the cases where the
pressure changes but slowly, as in those powders known as
slow-burning powders.
Noble's Experiments.
In 1869, Capt. Noble, R. A., prepared a M. L. gun as
.described, Chap. VI. Crusher gauges were placed in the
holes leading to the chamber, and the other holes were
provided with the apparatus also given in Chap. VI.
By observation and interpolation, a table of spaces and
times was formed so as to make A x constant=6, 10°^, as
follows:
7J ^^
Av
/- ^ a
X
/
At
At
A V
logdt
dt
^ Ttr^g
mm.
sec.
sec.
m. s.
m. s.
*
m. s.
kil. per
c=] cm.
0.00
6.10
0.0000000
0.0018182
0.0018182
8.85
0.0005590
7.56
4.88327
9891
271
12.20
0.0023772
10.91
0.0002528
9.02
4.61517
22082
005
18.30
0.0026330
19.33
* The values of dt are obtained by interpolation. That of the mean
acceleration for the first value of Az^, viz., A/=
0.0023772
=0.0011886
would evidently be too large, and the corresponding value for /=186.5
would be too small. The method of interpolation is similar to that here-
after described in Exterior Ballistics.
VII. — l-KESSTTRE GAUGES. 17
Fig. 15, represents the curves obtained in a 10 in. gun
firing a 300 lbs. projectile with fine (R. L. G.), and coarse,
(Pebble) powders.
The muzzle velocity of the projectile was in both cases
practically equal.
Comparison of Results.
The calculated pressures agreed closely with those ob-
served in the gauges placed near the base of the projectile
when at rest; and those observed at the base of the bore
considerably exceeded those observed near the base of the
projectile. ^^^. Chap. XI.
VIII. — PHENOMENA OF CONVERSION.
CHAPTER VIIL
PHENOMENA OF CONVERSION.
Phenomena.
For purposes of analysis the conversion of gunpowder
into gas may be considered under tliree heads, viz.: Ignition^
Inflammation and Combustion,
Definitions.
By Ignition is meant the setting on fire of a particular
point of a grain or charge.
By Inflamination is meant the spreading of the fire from
point to point of the surface of a grain, or from one granu-
lar surface to another throughout the charge.
By Combustion is meant the passage of the inflamed
surface throughout the substance of each grain.
IGNITION.
Gunpowder is the most refractory of the explosives; it
ordinarily requires a temperature of 300°. Its ignitibility
varies inversely:
1st. With the amount of moisture present.
2d. With the smoothness and sphericity of the surface.
3d. With its density.
It also varies with the character of the charcoal.
COMBUSTION.
Definition.
By velocity of combustion is meant the rate of motion of
the inflamed surface in a direction normal to that surface.
Owing to the impossibility of determining this within the
VIII. — PHENOMENA OF CONVERSION.
gun, the velocity of combustion of different kinds of
powder in the open air is taken by the manufacturer as a
rude means of comparing their combustibility.
Determination.
If the size of the grain permits the time of its burning to
be accurately determined, this simple method is preferred;
since it resembles most closely the actual conditions of prac-
tice. Otherwise, we may extend the time to be measured
by burning, like a candle, a prism of press cake having its
sides greased to protect them from the flame; or else, we
may use a tube rammed with the pulverized mill cake of
the same density as that of the powder to be tested. So
determined, the velocity is found to be about 0.4 inch per
second.
Nature of Combustion. 1. In Air.
This experiment proves that the composition burns in
parallel layers at a uniform rate; so that the combustion of
a spherical grain would resemble the peeling of an onion.
This fact is frequently illustrated on the proving ground,
where burning grains of powder are projected from the gun
with sufficient force to penetrate deeply into wooden
boards. Should they fall in snow, their appearance will
plainly indicate the superficial nature ot their combustion.
2. In Gun.
It is important to remember that the velocity of combus-
tion within the gun is very much greater and less uniform
than that in the open air. The process resembles roughly
the absorption of water by a porous substance when under
variable hydrostatic pressure. The effect may be, not only
to accelerate the velocity of combustion, but also, by break-
ing up the grains, to increase the burning surface; as we
crush sugar to facilitate its solution.
The velocity of combustion is supposed to vary directly
with the intensity of the gaseous pressure.
VIII. — PHEKOMENA OF CONVERSION.
CIRCUMSTANCES AFFECTING THE VELOCITY OF COMBUSTION
IN AIR.
Varying Conditions.
Under similar circumstances the velocity of combustion
of homogeneous powder is constant. It varies however,
with the purity^ proportions^ incorporation^ density and con-
dition of the powder as follows;
1. Purity.
The nitre and sulphur should be pure, or nearly so. The
part that charcoal plays depends upon its combustibility.
This is determined by finding the velocity of its combus-
tion, when incorporated with a due proportion of nitre in
such a tube as above described.
2. Proportions.
By varying the proportions, all velocities up to 0.55 inch
per second can be obtained.
The proportions usually adopted are those that give the
greatest volume of gas in a given time, because the mass
burned is the greatest, and because each unit of mass gives
the greatest volume of gas.
3. Incorporation.
Prolonging the incorporation increases the velocity at a
rate which increases as the proportions approach those
adopted.
4. Density.
With each set of proportions a density is soon reached
that corresponds to the maximum velocity. Beyond this
density the velocity varies inversely as the density, at a rate
which increases as the proportions approach those adopted.
The increase in superficial density due to glazing dimin-
ishes the velocity of combustion; provided that the dust
formed in the process be removed.
VlII. — PHENOMENA OF CONVERSION.
5. Condition.
The velocity increases with the porosity of the powder.
See page 2. The porosity may result from the evaporation
of water, alcohol, or vinegar, added to the substance before
pressing it. When porosity is carried to the point of fria-
bility, the consequences described, page 2, may be expected.
AVhen oils, gums, or resins are added, or when an excess
of water remains in the composition, the velocity of com-
bustion is diminished. An excess of water permits the nitre
to segregate and to neutralize the effects of incorporation.
Re7nark<
These variations should be carefully studied, as upon
them depend the most important characteristics of gun-
powder.
Emergency Powder.
For example; during the Franco-German War of 1870, it
was found necessary to increase, far above their normal
capacity, the product of the powder mills remaining in the
hands of the French.
This was accomplished by reducing the time of incor-
poration under the wheels, besides calling into use the stamp
mills and rolling barrels formerly employed for this pur-
pose.
The effect of less thorough incorporation upon the
velocity of combustion was neutralized by reducing the
density of the powder.
This answered well where the powder was not intended
to be stored, and where the capacity of the chambers in
which it was to be fired permitted a corresponding increase
in the volume of the charge.
The differences of the effects upon the gun and its pro-
jectile, resulting from varying the phenomena of combus-
tion, are described in Chapters X and XI.
VIII, — PHENOMENA OF CONVERSION.
INFLAMMATION.
Hypothesis.
The inflammation of a single grain is generally assumed
to be instantaneous, and so is that of a charge of powder;
unless the time of its inflammation bears so considerable a
ratio to that of its combustion that the total time required
for the conversion of the charge into gas is sensibly in-
creased.
Experiment.
The nature of the process may be studied by determining
the time required to inflame trains of powder of known
lengths under various conditions.
Varying Conditions.
The velocity of inflammation is found to vary:
1. With the disposition of surrounding bodies.
2. With the size and shape of the grains.
3. With their composition and constitution.
1. Confinement.
The heated gases, evolved by ignition, follow in their ex-
pansion the line of least resistance. If they are confined,
so that this line coincides with that along which the powder
is disposed, its rate of inflammation is increased. Thus, the
velocity of inflammation of a train is increased by firing it
in a tube instead of in the open air. It is still further
increased when the cross-section of the tube is not entirely
filled; and when the bottom of the tube, near which the
train is ignited, is closed, as in a gun.
2. Size and Shape of Grain.
The size and shape of the grain affect both the force
propelling the gases and the resistances which they encoun-
ter. In the first case, the size and shape of the grain affect
the amount of gas evolved in equal successive times and
also the ignitibility of the unburned grain; in the second
VIII. — PHENOMENA OF CONVERSION.
case, they affect the size and shape of the spaces between
the grains. So that, in fine powder, although the gaseous
pressure may be greater, the resistance to the passage of the
wave of inflammation may also be greater. In coarse pow-
der the converse may be the case. The velocity of inflam-
mation should therefore be determined by experiment.
It is now much less important than when muzzle loading
guns were in use.
If the charge be made of mealed powder compressed,
there will be no interstices; and the velocity of inflammation
and that of combustion will be the same.
If it be of concrete powder, the velocity of combustion of
the entire grain will be that of the inflammation of the con-
stituent grains, and will be greater than that of the com-
pressed mealed powder above referred to.
This ratio was found to be as 1.4 to 1.0.
3. Composition and Constitution.
The velocity of inflammation is affected by variations
in the purity and proportions of the ingredients, in the
thoroughness of their incorporation, and in the density of
the powder, in so far as these affect its velocity of combus-
tion and its susceptibility to ignition.
IX. — NOBLE AND ABEL's EXPERIMENTS.
CHAPTER IX.
NOBLE AND ABEL'S EXPERIMENTS.
From 1868 to 1874, Captain Noble, R. A., and Mr. F. Abel,
the chemist of the British War Department, made a series
cf experiments upon gunpowder that have become his-
torical.
NATURE OF THE EXPERIMENTS.
These experiments were conducted on the principle,
general in all experimental comparisons, of keepmg all con-
ditions constant except that of the variable under consideration.
Although their ultimate object was to determine the
behavior of fired gunpowder in the variable volume behind
the projectile in a gun, this principle required that their
preliminary experiments should be conducted in closed
vessels, the capacity of which was invariable and accurately
known.
VARIABLES.
They accordingly varied: —
1. The composition of the powder.
2. The size of its grain.
3. The mass of gunpowder exploded in a given volume,
or the density of loading.
FUNCTIONS.
Under these different circumstances they observed: —
1. The maximum pressures per unit of area.
2. The composition and condition of the products of
combustion.
2 IX. — NOBLE AND ABEL's EXPERIMENTS.
3. The specific volume of the gases formed, viz^ at a
pressure of one atmosphere and at 0°.
4. The quantity of heat evolved by the combustion.
CONCLUSIONS.
From the observed states of the functions corresponding
to particular values of each variable they sought to
determine the law expressing the relation between pres-
sures, volumes and temperatures in closed vessels, with the
view of applying it to the variable conditions existing in
guns.
METHODS FOLLOWED IN THE EXPERIMENTS.
VARIABLES.
1. Composition of Powders.
Four of the six kinds of powders tried were approxi-
mately of the usual composition. The others differed
notably as seen by the following table:
COMPONENTS. POWDERS.
Four English. Spanish. Blasting,
Nitre, 74
Carbon, 12
Sulphur, 10
Water, H, O, Ash, etc., 4
100 100 100
2. Size of Grain.
The principal experiments in which the size of grain
entered as a variable were those in which comparisons
were made between R. L. G. (Rifle, large grain) and the
Pebble powders referred to Chap. VII. The linear dimen-
sions of these powders were about as 1 to 3.
3. Density.
It is evident that the results of the experiments were
largely dependent upon the relation existing between the
75
62
9
18
12
15
4
5
!X. — NOBLE AND ABEL's EXPERIMENTS.
mass of the charges and the volumes in which they were
fired. This requires a discussion of the density of powder
which is named under three heads.
1. Specific Gravity.
By density simply, or d, we mean the specific gravity of
the press-cake, or that of the individual grains, referred to
water. This in practice ranges from 1.68 to 1.85. The
maximum attainable density calculated from that of the
ingredients of gunpowder united in their ordinary propor-
tions, is 1.95.
2. Gravimetric Density.
By this term, or y^ we mean the density referred to water
of grained powder, including its interstitial volumes; or,
calling w, the weight in pounds of one cubic foot of the
loose powder.
^~ 62.425 ^^
The gravimetric density is sometimes expressed by the
weight in ounces of one cubic foot of the loose powder.
The gravimetric density of powder is important when it
is to be used in a limited 'volume as in the cartridges for
breech-loading small arms and in explosive projectiles. It
is evident that the form of grain and the amount of settling
affect the interstitial volumes and hence its value. For
loosely piled powder of irregular granulation it is about 0.9.
Specific and Interstitial Volumes.
The amount of the interstitial volumes, which, as seen in
Chap. VIII, affects the rate of inflammation, may be de-
termined as follows:
Let F, represent the volume of the powder when loose;
v,^ its specific volume, or its volume when compressed to a
uniform density, 6 ; and v' ^ the sum of the interstitial volumes :
then, since w = F y = z^, (5.
IX. — NOBLE AND ABEL S EXPERIMENTS.
d : y :: V W or v=y -k- (2)
whence v'= F-v= F ^^"^^ (3)
Ordinarily, d is about 1.8; and, when the powder is loosely
y
piled, V is about 0.9. In such a case v=v^= -^.
Noble conducted his experiments with powder so closely
packed that y was sometimes equal to unity: in such a case
v' was sensibly equal to 0.44 F.
3. Density of Loading.
By this term, or A , we express the relation between the
mass of a charge of powder and the volume in which it is
fired.
If the values of S and y were constant, it would suffice to
say that the cavity holding the powder was, say, one-half,
three-quarters full, etc. This was the method adopted by
the early experimenters.
But the quantity of matter in a given volume of grained
powder may vary from both the causes named.
The value of A is therefore taken as the ratio of the
weight of the powder fired, to the weight of water at its
maximum density which would fill the volume in which the
powder is fired. Calling this volume expressed in cubic
feet F, and expressing w^ as before, in pounds, we have
w
^ ^ Fx 62.425 (^^
It is usual to give the linear dimensions of guns in
mches; therefore calling z;= Fx 1728, the volume in cubic
inches, we have
• ,^^^ (5)
This value of A is of constant application and must be
remembered.
IX. — NOBLE AND ABEL's EXPERIMENTS.
APPARATUS.
The vessels employed were strong steel cylinders as
shown in Fig. 1. Each one contained a firing plug, F^ with
a conical stopper, /, insulated from 7^ by a washer, w, and by
sheet of tissue paper wrapped around its body. Another
conical screw plug, P, carried a crusher gauge, C.
The object of the form given to F and P was to facilitate
their removal; since a very slight motion would free them
from the walls.
The charge was ignited by an electric igniter, /.
After the firing the vessel was immediately conveyed to a
calorimeter; or a smaller vessel. Fig. 2, could be fired
under water.
FUNCTIONS.
1. Pressures.
These were determined by the crusher gauge, and the
observed results compared and corrected by the methods
used in experimental research.
2. Nature of Products.
Small samples of gas were drawn off for analysis through
the tube, E, opened by slightly unscrewing the valve e.
The initial liquidity of the non-gaseous products was
determined by tipping the cylinder in various directions
soon after the explosion, and by observing the appearance
of the solid crust when the vessel was finally opened.
3. Volume of Gases.
The specific volume of the gases was determined by a
gasometer. Fig. 3. The long wTench, w, passing through
the stufhng-box, sb^ was used to unscrew P^ immediately
after the explosion.
4. Heat.
The quantity of heat evolved by the conversion was
determined by immersing the vessel in a calorimeter con-
6 IX. — NOBLE AND ABEL'S EXPERIMENTS.
taining a known weight of water of known temperature,
and by noting the resulting rise in temperature.
RESULTS OF THE EXPERIMENTS.
STATES OF THE FUNCTIONS.
1. Pressures.
For all kinds and sizes of powder the pressure was found
to be practically constant for equal densities of loading, or
the force o( SiW the powders was the same. When A=l,
the force was about 6,400 atmospheres, or 43 tons, or
96,000 lbs., per square inch.
2. Products.
The following table* gives, by weight per cent, the mean
proportions of the products resulting from many experiments;
PRODUCTS. KINDS OF POWDER.
Gaseous. Tour English. Spanish. Blasting.
CO2,
CO,
N,
Various,
Total Gaseous,
Non-Gaseous.
K, CO3,
K2SO4,
Ka S,
Various,
Total Non-Gaseous, 66 62 49
From the appearance of the cavity after firing, the non-
gaseous products were supposed to be suspended at the
instant of the explosion as a highly heated liquid spray
which eventually assumed a solid form. In cooling it was
26
25
23
3
1
15
11
11
9
4
1
4
44
38
51
34
22
19
12
30
6
6
17
4
5
13
*NoTE. — The relative proportions of the total gaseous products and of
CO, should be learned. See Chapter II,
IX.-
supposed to shrink from about 0.6 the volume of the entire
charge, or 0.6 F, page 3, to about 0.3 V.
Confining our attention to the typical English powders it
is significant to observe that very nearly the same propor-
tions were concluded to exist between the volumes occu-
pied by the gaseous and non-gaseous products at the instant
of the explosion, as were found to exist between the weights
of these products and between the interstitial and specific
volumes of the charge.
That the non-gaseous products did not, by their volati-
lization, augment the volume of the gases was inferred from
their behavior when exposed, solid, in a Siemen's furnace,
to a temperature of about 1700°. At this temperature
which, although the highest available, was about 700° lower
than that determined by calculation, the solids swelled to
nearly twice their volume, but did not volatilize.
3. Volumes. 4. Heat. ^
The relations between the specific volumes of the gases
and the calorific values of the powders appear from the
following table which illustrates the curious fact, noted in
Chap. II, that their product is approximately a constant
quantity. The volumes are referred to that occupied by tlie
powder when A = 1. See note 1, page 13.
Kind of Powder. Specific Volumes. Heat Units Products,
or vq. or H.
English powders, 264 737 194568
Spanish powder,, 234 767 179478
Blasting powder, 360 517 186120
Had the experimenters known the specific heat of the
products of combustion when at a constant volume, or C^,
the absolute temperature of the conversion, or Tq, might
have been determined from the general equation,
If
IX. — NOBLE ANt) ABEL*S EXPERIMENTS.
but, although the same products were always formed, they
occurred in such varying proportions, even when all the
conditions were as nearly as possible identical, that no
certain conclusions could be made. Chap. II, page 7.
Also, by taking the mean specific heats of the mean of
the non-gaseous products, when in a solid form, and also of
the gases, a temperature was computed which was mani-
festly too great. The experimenters accordingly adopted
the following course in which the deductions of theory are
corrected by experiment.
Temperature of Explosion.
Assuming the general equation for the work of perma-
nent gases subjected to changes in temperature, or —
pv=^rt, (6)
in which r is a constant, and t is reckoned from absolute
zero; let us express/ in atmospheres.
The preceding table gives for the English powders a
mean value of r= (264 = v) (1 =/) v (273 = /) = 0.967.
Substituting the values of v and / for A zz: 1, we have —
/= (6400) (0.4) ^ 0.967 = 2646° absolute, = 2373° C
This was verified for varying values of A and by the ex-
posure to the temperature of the explosion of very fine
platinum wire which melts at about the temperature above
determined.
CONCLUSIONS.
Fundamental Hypothesis.
The remarkable compensation between the volumes of
gas generated and heat evolved permitted Noble and Abel
to apply to these gases the laws of Mariotteand Gay-Lussac;
provided, that from the volume of the chamber in which the
explosio7i occurred was subtracted the volume occupied by the
non-gaseous residue.
IX. — NOBLE AND AP>EL S EXPERIMENTS. 9
Remarks.
This conclusion, although simplifying the labors of the
experimenters, and useful for a general discussion like the
present, is now believed to depend upon a compensation of
errors.
It is now believed that the solid products are volatilized
and probably dissociated, and it is known that Mariotte's
law does not apply to the pressures observed in guns.
Still the latest researches lead to practically the same con-
clusions reached by these experimenters.
EXPERIMENTS IN GUNS.
The experimenters found that when the gases expanded
into a varying volume, as in the gun, results similar to those
above described were found, vk.:
1. Products.
That the nature and proportions of the products remained
the same as in a closed vessel.
2. Working Substance.
That the work on the projectile may be considered to be
due to the elastic force of the permanent gases.
3. Source of Energy.
That the heat evolved by the non-gaseous residue main-
tains the gases at a constant temperature during their expan-
sion, which, therefore, is isothermal.
This is essentially the hypothesis of Hutton, made a cen-
tury ago. For want of suitable apparatus Hutton erred
greatly in his deductions from this hypothesis,
4. Theoretical Work.
The total theoretical work of the permanent gases, when
indefinitely expanded, was computed to be about 486 toot-
tons per pound of powder.
10 IX. NOBLE AND ABEL's EXPERIMENTS.
This is nearly the result given by the table on page 7.
Only from 13 to 20 per cent, of this work can be realized
in practice. See note 2, page 13.
6. Loss of Heat by Absorption.
The quantity of heat lost by absorption was approxi-
mately determined by plunging into a calorimeter a field
piece, after firing from it a number of rounds in rapid suc-
cession.
The loss was found to vary directly with the ratio of the
cooling surface to the weight of the charge, and also with
the time of travel in the bore.
It varied, per unit of weight of the powder fired, approx-
imately as follows:
Gun. Loss in H. ^ Energy.
10 in. M. L. R. 25 3.5
12 pdr. B. L. R. 100 14.0
0.45 in. B. L. R. musket' 250 35.0
6. Pressures.
The experimenters confined themselves to the prediction
of velocities. The determination of the actual intensity of
the variable pressure during the progressive combustion of
the powder in a volume varying with the position of the pro-
jectile during combustion was determined in only a few
special cases. The important law by which this pressure
varies, upon which modern guns are constructed, was left
unsolved.
The methods of M. Emil vSarrau, of the ^'- D^partement
des Poudres et Salpltres^'' which depend rather upon dynam-
ical than chemical laws, corrected, like those of Noble and
Abel, by experiment, are now generally followed where ac-
curate prevision, both of pressures and velocities, is required.
The older methods are adopted in this text, as they permit
the presentation of some of the more important phenomena
of fired gunpowder in a relatively simple form.
IX. — NOBLE AND ABEL's EXPERIMENTS. 11
DEDUCTION OF THE VARIABLE PRESSURES IN A
GUN.
Hypothesis.
It has been shown in Chapter VIII. that the conversion
of gunpowder is not instantaneous. Yet, on account of the
difficulty of determining the circumstances of the motion of
the projectile during the period of combustion, or x=q) (t)
and the rate of combustion under the varying pressure to
which the powder is exposed, or gz=/ (t) it is best to begin
by assuming that the conversion is instantaneous, and to cor-
rect the results of computation by experiment. See note 3,
page 13.
Assuming then, the proportions of solid and gaseous pro-
ducts previously given, and that the change in pressure is
due to the change in volume in rear of the projectile (which,
under the isothermal hypothesis, acts like a piston moving
with variable velocity under some external force), we may
deduce the following relation between the pressure and the
mean density of the products of the explosion.
Let / represent the intensity of the gaseous pressure in
tons per square inch, and
Wy the weight of the charge in pounds;
Vf the variable volume behind the projectile in cubic
inches;
v'f the volume occupied by the non-gaseous products in
cubic inches;
<^, the density of these products referred to water;
d, the density of the gases referred to water and supposed
to remain at a constant temperature.
jff, the ratio -^ assumed under Mariotte's law to be con-
stant.
Deduction.
From the general expression for density we have
12 IX. — NOBLE AND ABEL's EXPERIMENTS.
^ 0.44 wx 27.68 12.18 a/ ,
d— -. = -J- ; and
v—v v—v
^, 0.56 wx 27.68 , \h.hw
d'^ -, •••^^--^7-; and
^ 15.5 w
" — n^'
Multiplying both numerator and denominator of the value
of/ by
27.68 2.2724
12.18 z;~ V
, we have
p=R ^ -. (7)
2.2724-1.2726 -^
The ratio, R^ is found, by experiment, not to be absolutely
constant; but, by selecting from Noble's experiments in
closed vessels, suitable values of / and A in pairs, and by
substituting these values in Eq. (7), we may obtain two
equations, containing two unknown quantities, from which
we find (See note 4, page 13.)
7?=32.18 ^'=0.824.
These values substituted in Eq. (7) give, after reduction,
_ 1 *
A
Which, for convenience, may be placed under the form
/= 1 (9)
0.0025571 - -0.048
w
Equations (8) and (9) give remarkably close approxi-
mations to all but the very highest pressures found in Noble's
experiments in closed vessels.
*log 0.070618 ="3.8489170. flog 0.0025571 = 3^4077557.
IX.— NOBLE AND ABEL's EXPER1M£NTS. 13
COROLLARIES.
V
1. By substituting in Eq. (9) proper values for ^= — ^>we
may construct a curve, as in fig. 4, which will give the pres-
sures at different points along the bore of the gun under the
assumptions noted, page 11.
Should the piece be chambered, the value of x\ the re-
duced length of the chamber =.Yo\vimQ. of chamber-^ ;r t^ must
replace its measured length.
2. It is evident that the value of the initial ordinate is
determined by the value of the density of loading, A.
3. Also that, knowing by experiment the intensity of the
maximum pressure, and the charge, we may determine
approximately the corresponding position of the projectile.
__ ^ [l+(/X 0.04 8)1
Smce X — ^^py^ 0.0025571 '
4. Also that we may determine the charge required to
burst a closed vessel, like an explosive projectile, when its
resistance to rupture is known.
NOTES.
1. Page 13. — The experimenters ascertained that the erosion of the
bore, caused by the rush of the gases past the projectile, increases directly
with the factor H, and inversely with v^.
Since modern steel guns fail rather from erosion than from bursting, it
is possible that the large values of H, now generally sought, may be
ultimately diminished in favor of z/q.
That is, that the guns have a surplus of strength that may profitably
be used to favor their endurance under erosion.
2. Page 10.— Taking y=1390 ft. -lbs. for !« C we have
Q=-U[= '^^TXISQO ^ ^g,^ 3 Qj. 94 ^^^^^ oi4:%Q. foot tons.
2240 2240
3. Page 11. X and a signify respectively the variable space passed
over by the projectile and the variable surface of the burning grains com-
posing the charge. Chap. XI, pp. 2, 3, 4.
4. Page 12. — For recitation at the board the numerical values after
Eq. (7) may be represented by symbols.
X.— eoMStrstiON IN Alft.
CHAPTER X.
COMBUSTION IN AIR.
Single Grain.
We know from the experiment in Chap. VIII that in air,
gunpowder burns only superficially, so that the burning
under these circumstances of a spherical grain may be
likened to the exceedingly rapid peeling of an onion.
Considering, for the present, all solid grains to be repre-
sented by their equivalent spheres, the radius of any sphere
will be equally shortened in equal successive times, but the
surface and the volume will vary in a higher ratio to the
time.
Accordingly let Fig. 1 represent the central section of
a hom.ogeneous spherical grain burning with a uniform
velocity of combustion which in the variable time, /, will
reduce the original radius R, to r, and the original surface
iS", to s. Let the time required for the combustion of the
entire grain be r.
Then ^: j::i?2 : ;^::t2 : (r-/)2, or
^=^{r-t)\ (1)
By differentiating Eq. (1) with respect to s and / we have
It may be shown from Equations (1) and (2) that the
curve, Fig. 2, expressing the relation s=/{f), is a parabola
referred to a system of rectangular axes; one of which, the
axis of times, coincides with the tangent at the vertex of the
parabola, and has upon it the origin, O, at a distance from
the vertex =r.
X. — COMBUSTION IN AIR.
The rate of change of the ordinate of the curve is the
same as that of the surface of the burning grain.
The summation of the successive ordinates of the curve,
corresponding to any value, /, will be equal to the area
O Ssf; and since the ordinates represent the correspond-
ing successive surfaces, this area will be proportional, either
to the mass or volume of the grain which has been burned
up to the time /, according as the density of the powder is,
or is not considered.
y'' dw
sdtj-j- =s, or the rate at
which the mass of gas is increasing at any instant,or the
rate of conversion, is proportional to the corresponding
surface.*
The total area O S r= — - — will be proportional to the
o
original mass or volume of the grain.
Number of Grains Varied.
Such a relation, once established, would be true for all
equal grains composing a charge, and would therefore be
true for the whole charge, but the rate of conversion would
vary with the size of the charge as shown by curves 1 and
2, Fig. 3. In these, 1, represents such a curve as shown in
Fig. 2, for a single grain; and 2, the same for n grains com-
posing a charge.
Size of Grains Varied.
If, in a charge of a given weight composed of spherical
grains of a given density, the -size only, of the grains be in-
*If the grain be not homogeneous, and burn with a variable velocity
the rate of conversion will vary with the product of the surface, J, of the
density, b, and of the velocity of combustion ft), or
= J X X w.
dt
In this case the curve will no longer be a parabola,
X. — COMBUSTION IN AIR.
creased, the sum of the granular surfaces, ^ S, will be in-
versely proportional to the radius of the grain.
•For W=n v d, and v= — jr— .-. W=
or^=
3 3 '
3 W 1^
nS ' r
or r
If we represent by ^ the sum of the initial granular
surfaces of a charge, and by 6 the sum of the successive
granular surfaces of the same charge during its combustion;
Fig. 4 may represent by curves 1 and 2, respectively, the
relation G=f {f) for charges of equal weights composed of
grains of different sizes.
Objections to increasing Size of Grain.
The effect of increasing the size of the grain is to make
the powder relatively slow ; or, as it is called with reference
to its action in the gun, 7nild or progressive. This diminishes
the value of --z- by increasing the value of r.
The objection to this will hereafter appear; it will suffice
here to say that it may require the gun to be of inconvenient
length.
Alternatives.
The following methods have been proposed for regulating
the rate of conversion without, in all cases, increasing the
value of r.
Constant Rate.
1. A constant rate would evidently be attained by form-
ing the powder as a prism and confining the burning area to
that of its cross section. This result is approached in the
Zalinski pneumatic gun, in which compressed air from a
large reservoir, expands continuously into the volume be-
hind the projectile. Also in the steam engine.
X. — COMBUSTION IN AIR.
2. An approximation to a constant rate, with a small value
of r, has been sought by forming the powder into volumes
of which two dimensions considerably exceed the ihird. The
French, Castan, powder and the American, LX, powder are
so formed.
Increasing Eate.
The rate of conversion may be increased by causing the
burning surface to increase:
3. By igniting the grain from the interior, and protecting
the exterior surface from the flame by forming the grains
into hexagonal prisms closely packed together, fig. 5. The
perforations are continuous flues, facilitating inflammation.
This is Rodman's powder.
4. By diminishing the density of the grain toward its
center, Chap. III., or by facilitating its disruption after
ignition.
These cases may be represented by the correspondingly
numbered lines on figure 6.
COROLLARY.
Supposing the charge to consist of n equal spherical grains,
the proportion of the whole charge that will be burned in the
variable time, /, may be determined as follows :
The original volume of the charge is, F= n ^ i: R^ \ or,
assuming, as before, that the velocity of combustion is unity,
V=z n -^ TX r^, the unburned volume at the end of the time,
t,v7'i\\hev,-n^7T{r—ty=,v{l—[\ - Therefore, the
volume burned will be, z/'= V—Vf^z V\ 1 — ( 1 — - j (4)
Similarly w' = ^F 1— ( 1— ^)' 1 - (5)
The curve whose ordinates express the relation w' z=. f {t)
will be of the form shown in figure 7, and figure 1, chap. XII.
XI. — COMBUSTION IN A GUN
CHAPTER XI.
COMBUSTION IN A GUN.
PRESSURES.
Comparison to Steam.
For purposes of illustration, the action of gunpowder,
when burning in a gun, may be compared to that of steam
in the cylinder of a steam engine; and the pressures,/, at
different lengths of travel, x, of the projectile in the bore,
may be represented by the ordinates of a curve which
expresses the relation jf=f [x), in the manner used in the
indicator diagram of the steam engine.
The operation may be conveniently analyzed by dividing
the volume of the bore into two portions, viz.:
1st. That through which the elastic gases are being
evolved from the burning powder, called the combustion
volume.
2d. That through which these gases are expanding under
the elastic potential acquired during combustion. This may
be called the expansion volume.
Thus, the circumstances during the passage of the pro-
jectile through the combustion volume correspond to the
admission of steam to the cylinder of a steam engine, and
the completion of the combustion to the action of the valve
which cuts off the supply of steam. The subsequent expan-
sion in both cases is limited by the length of the cylinder.
This important difference exists; that the expansion,
which in steam is treated as adiabatic (without loss
of heat except from external work), and which, there-
fore, leads to a loss of temperature due to the work done,
XI. — COMBUSTION IN A GUN.
is, in the gun, supposed, from Noble and Abel's experi-
ments, to be isothermal^ and, therefore, under Mariotte's
law.
DISCUSSION.
Hypotheses.
In the following general discussion we will, for simplicity,
begin by assuming that the projectile starts freely from its seat.
We will neglect the variable volume of the liquid residue
and that of the powder remaining unburned at any time.
We will also assume that the inflammation is instanta-
neous. See Chap. VIII.
Notation.
Taking the origin of co-ordinates at the origin of motion;
X will represent either the path of the projectile or the
volume described by the translation of its maximum crosr
section.
The volume of the chamber, ^, or the initial volume, is
composed of two volumes, viz.:
c, the volume actually occupied by the charge of powder
including its interstitial spaces.
c\ any excess of volume besides that required to hold
the charge. Therefore, k=zc-\-c\ and, for the reduced
k
length of chamber^ we have x, -=l ^ , in which r is the
radius of the bore. We shall first take c' = O.
Let w represent the weight of a charge of powder which
will be consumed in a time r, and let w' be the variable weight
of w converted into gas at the end of any time /.
Let (S represent the corresponding sum of the burning
surfaces as in Chap. X, and '2 the sum of the initial sur-
faces.
Let / represent the variable intensity of the gaseous
pressure per unit of area on the base >f the projectile; and
XI.— COMBUJ^TION m A GUN.
assume any particular value o. / to be uniform throughout
the volume occupied by the gases, the density of which is d.
Let/ be taken in such units that R^ Chap. IX, be equal to
unity.
Let W represent the weight of the projectile, the radius
of the cross section of which is r\ the variable velocity of
which, in the bore is v\ and, at the muzzle of the gun is V.
Let q and Q represent the quantities of work done upon
the projectile to give it the velocities v and V.
FORM OF PRESSURE CURVE.
Upon firing the charge the combustion volume is gradu-
ally filled with gas, the density of which will vary directly
with w' and inversely with x-\-c\ so that we may write
w'
Differentiating this equation, considering /, w* and x as
variables, and dividing through by dx^ we have
dp __
dx x-\-c
1 i dw* w* \
'^c\dx x^cX
(2)
(3)
But, since q=f p dx^
dp _ _1_^ / dw'—dq \
dx ~ x-\-c \ dx J
Or, dividing both numerator and denominator of the
expression in the parenthesis by dt and remembering that
dw'
dt
Similarly,
dp _ 1 / dq \
dx '~ {x^c)vy dt )' W
dp
No simple law has yet been discovered connecting (T, x
and /, and these equations cannot, therefore, be integrated;
XT.— COMBUSTION m A GUN.
but, remembering that (T is a decreasing function, and q
an increasing function of /, a conception may be had of the
form of the curve, the ordinates of which express the
relation /=/ (^).
The inclination to the axis of X will be greatest at first
when 6 is large, and x and ~- =p v are small. It will be
Oy or / will be constant, when the gas is evolved just fast
enough to compensate for the increasing volume. From
this point the conversion is not rapid enough to keep up
the maximum pressure, so that the pressure will fall off
until a=.Oy as at «, Fig. 1, from which point the curve will
be an hyperbola with the axis of X as an asymptote, since
p becomes equal to a constant, w, divided by x-\-c. By
the law of continuity, a should be a point of inflexion and a
point of tangency between the combuscicn and the expan-
sion curves.*
The same results will follow when / is taken =/' {t), ex-
cept that the inclination of the tangent to the curve will
vary more gradually.
I. PRESSURES DURING COMBUSTION.
Effect of Size of Grain.
Although we do not know the law which, in the gun, con-
nects (T=/(/) and x = Qf (/); experiments with Noble's and
Ricq's apparatus demonstrate that, when nearly equal charges
of powder, a and b, in which H^ > Z^^ are fired ; for small
♦The parenthetical expression refers to the relation between the poten-
tial energy of the unburned powder and the kinetic energy of the projec-
tile ; for n, the potential energy of the charge must always be equal to
7r = /(CT), that residing in the unburned charge; -]- q=f^ (v), the work
already done at any instant; -\-e=/^^ (/), the work which the elastic
potential of the gases is capable of doing; or H =7r -j-q-\-e.
XI. — COMBUSTION IN A GUN.
values of x and /, cp (/) changes but slowly for considerable
variations in/" (/).
The small change in the form of cp (t) for a given change
in the form of / (/) is probably due, on one hand, to the
relative constancy of the initial resistances to motion, or
the molecular work (Michie, Art. 25), and on the other hand,
to the great changes in / {t) resulting from the cumulative in-
fluence upon the velocity of combustion of high pressures
when (7 is large. Chapters VIII., X.
If, therefore, during the critical period of combustion, we
assume that qp (/) is nearly constant for all sizes of grain;
V, and therefore ^, may be taken as independent of o. Con-
sequently, Eq. 4 shows that during combustion, the inclina-
tion of pressure curves corresponding to different values of
Z will be an increasing function of a ; or for equal charges,
the smaller the grain, the steeper the curve. Similar reason-
ing shows that it will also be higher.
Experiine7ital Illustration.
This may be re'presented by fig. 2, derived from Noble's
experiments, in which a represents, by its ordinates, the suc-
cessive surfaces of a charge of fine-grained powder burned
in the air, its initial portion only being represented. The
curve a' shows the effect produced upon its burning by con-
finement in the gun. Let b and b' similarly represent the
varying surfaces of an equal charge of coarse-grained
powder. Let a and /3 be corresponding curves representing,
by their ordinates, the velocities acquired by the projectile at
any time, /. For any time /, the area under a' or b' =
J a dt=w' ; and similarly the area under a ox (i=J vdt—.x-^c.
Under the circumstances named, although Z^=*^ Zy,, the
curves a. and |3 were nearly coincident in their initial por-
tions. These, which we shall term the v curves and the a
curves, have the axis of time m common.
XI. — COMBUSTION IN A GUN.
At any time /, which is less than tb, the time required for
the combustion of the powder ^, the ratio, =/» is less
for the coarse grained powder than for the fine. At t^ ^^d
Tb expansion begins ; at r^ the pressures from the two pow-
ders will be nearly equal to each other, since the same weight
of powder in each case is burned in nearly equal volumes.
Similar effects would follow the changes in a, indicated in
Chap. X., from whatever cause the rate of change of o was
varied.
The best results would be attained when both the <j and
V curves coincided in such a line as ^, fig. 2, since we
would then have the constant pressure sought for in the
ideal gun.
The effect upon pressures of varying the size of grain, or
the rate of burning in charges of equal weight, would be
represented by the curves a, b^ k, in fig. 3, in which the nota-
tion of fig. 2 is preserved.
Additional Illustration,
The principle is illustrated in figure 10, in which curves a
and b (which to avoid confusing the drawing are omitted), may
be imagined to result from Equation (5), Chapter X, and a'
and b' to be constructed from a and b^ in the manner indi-
cated in figure 2. The curves a and ^ express the relation
x=f' (/) as in figure 2 they expressed v=.f{t).
The ordinate t y' represents the proportionate part w', of
the original weight of the charge, w^ (represented by O 7v),
that has been burned in the time O t\ and / z' the volume, x,
through which the projectile has moved in the same time.
Similarly for the curves b' and /?.
The line ^^ is parallel to O T^ and at a distance from it, on
the scale of the axis JT, that is proportional to the volume of the
chamber.. Then^p-p-^ = -^ = ^=A.- and similarly
for the curves b' and ^.
X!. — COMBUSTION IN A GUN.
In figure 2 it is not possible to represent the constant of
integration, c,
2. PRESSURES DURING EXPANSION.
The locus of the pressures at the end of the several com-
bustion periods is the hyperbola H, fig. 3, the intersection of
which, with the axis of P^ is at a height (9/, corresponding
to 43 tons per square inch, and the parameter of which de-
pends upon the weight of the charge. Thus, the hyperbola
H' would be the locus for a charge greater than w, and its
vertical asymptote would be at a distance from 6?= —Xi—c
See figure 5.
Remarks.
1. The relative constancy of the v curves, in spite of con-
siderable variations in /, may be explained by considering
the gunpowder as a reservoir of potential energy. In this
— ^ — J , SO that v=J\^w')y while we
have seen that/=/^^(w').
2. It is probable that the work done during combustion
is proportional to the weight of the charge.
ADAPTATION OF POWDER TO GUNS.
The preceding discussion shows that if the size of the
grain remains constant, the pressure increases with the size
of the charge.
In order to compensate for this, General Rodman pro-
posed to increase the size of the grain as the caliber of can-
non of the same class increased.
This is the basis of the modern practice requiring special
powders for special guns.
XI. — COMBUSTION IN A GUN.
PASSIVE RESISTANCES.
Returning to fig. 1, we see that the area limited by the
pressure curve, the axis of X, and the muzzle ordinate at w,
will represent the work done by the powder under the cir-
cumstances named.
The greater portion of this work appears in the kinetic
energy of translation of the projectile; and, for simplicity in
the following discussions, all the work will be considered to
have been so transformed.
The difference between the work of the pressures and the
energy of translation, which, in practice, may amount to
about ten per cent, of the former, is due to the work of the
passive resistances ^ including the waste.
Eesistances.
The work of these resistances is equal to the sum of the
following quantities of work:
1. That done in giving rotation to the projectiles in rifled
guns and in causing recoil.
2. That done in permanently deforming the projectile and
the gun. The former is practically confined to rifled pro-
jectiles and is greatest in breech loaders.
3. That done in overcoming the friction of the projectile,
and in distributing the charge in the form of gas through-
out the bore.
Waste.
4. The waste is due to the absorption of heat by the walls
of the gun, and to the escape of the gases past the projectile
and through the vent.
Graphical Representation.
So that if we take a pressure curve, as in fig. 4, and draw a
line R R\ so that the area under it, corresponding to any
length of path x, shall represent the work of the passive re.
sistances during the motion of the projectile over that path,
XI. — COMBUSTION IN A GUN.
the segment r/, of any ordinate x p, will represent that por-
tion of the total pressure which gives acceleration to the
projectile and imparts to it kinetic energy proportional to
the area included between the two curves and any limiting
ordinate.
Remarks.
Band.
In breech-loading guns the initial resistance is consider-
able until the rotating band has entered the rifling; there-
after the resistance diminishes rapidly.
Example: In a 9.5 in. B. L. R. a charge of over 4 pounds
of powder failed to move the projectile; but a slight increase
in the charge gave it considerable velocity.
"Waste.
The loss of energy from absorption of heat by the gun
increases with the slowness of the powder; since with slow
powder the velocity of the projectile is less at the moment
of maximum temperature or pressure.
It varies inversely with the calibre, since with charges of
the same proportions the weight of the charge varies with
r*, while the surface varies nearly with r^.
The escape through the vent probably increases with the
slowness of the powder.
Instantaneous Pressure.
Variability.
From the discussion, Chap. VII., it is evident that the pres-
sure at any instant throughout the volume in rear of the pro-
jectile is not uniform, but increases toward the bottom of the
bore, as represented by the variable line/o/- Fig. 4.
Neglecting the passive resistances, the intensity of the
variable pressure at the bottom of the bore, generally known
as/o> can, by analysis, be shown to be very nearly equal to
/
(w \
10
XI COMBUSTION IN A GUN.
Considering the passive resistance/o is taken =// 1 + yTvi-
Supposition.
For an elementary discussion, like the following, such
differences in the instantaneous pressure, and the effect of
the passive resistances, once understood, maybe neglected.
So that the pressure at any instant upon the bottom of the
bore will be assumed to be that exerted at the same instant
on the base of the projectile, and all of it is supposed to be
utilized in giving motion to the projectile.
JV
The difference, p n r' a, evidently tends to compress
. . . ^
the projectile in the direction of motion, and its effect will be
most felt at the base of the column of metal moved.
Except in the next discussion, in which actual free vol-
umes are considered, the origin of co-ordinates is always
taken at the origin of motion; viz., at that section of the
bore occupied by the base of the projectile when the gun is
fired.
WORK OF FIRED GUNPOWDER.
It is not necessary in practice to separate the work of
combustion from that of expansion; but the total work which
may be expected from a given charge of powder may be
determined in the following manner.
Total Potential Work.
In fig. 3 the area included between the ordinate O P^ the
axis of X, and the hyperbola H at infinity, will represent
the total amount of work which this charge could perform.
Calling this i2, we see, from Chapter IX., that expressing,
as is usually done, work in foot-tons, and w in pounds,
/2=486 w.
Actual Potential Work.
If, instead of expanding the powder gases to infinity, we
limit the useful work of the expansion by placing the muzzle
XI. — COMBUSTION IN A GUN. H
as at m^ we shall have an area which will represent the
maximum potential work under the conditions existing in
the gun.
This, which in practice is not much over — , we will call Q.
Effective Work.
Now, if we fire the charge w in a gun, we shall give a
certain velocity F to a projectile W. Calling the amount
of kinetic energy so realized E^ we have
E=.
2^x2240
The ratio, -— = F, is called the factor of effect. It is
used, as hereafter explained, in anticipating the results of
certain changes in the piece and ammunition.
Fig. 3, shows by the triangular areas above the curves,
a, ^, k, the principal reason why 7^ < 1.
F is further diminished by the passive resistances.
MEASURE OF Q.
To deduce a formula for the potential work of the
powder gases when expanded in a gun of a definite length,
or the equivalent of the area Q^ we use the general equation
^—^dx. (6)
Substituting the ;i^alue of /, from Eq. 3, Chap. IX, and
for brevity replacing 0.0025571 by «, and 0.048 by by we
have, since all linear dimensions are given in inches,
G" (inch-tons) = ^
na d*
12
XI. — COMBUSTION IN A GUN.
(2" (inch-tons) ='^ ' '^^
Takinrj, in this case, the origin of co-ordinates at tne
bottom of the bore, integrating between x^, and x' , corre-
sponding to O' O and O' m^ fig. 1; substituting the value
of a^ and remembering that Q= ■^— , we have,
^'-23.9 ^3
e= 75.04 tt/, log ~ . (7)
^,-33.9 -,
Volumes of Expansion.
The subtractive term above, appears from the form of the
equation and can be shown to be the reduced length of the
residue,* or
/>=33.9^; (8)
pand x^/—x^—p: — =z n ^ number of
volumes of expansion, an important characteristic of a gun.
It is convenient to remember that p=: about -j^ the length
of the cartridge, if its diameter =d above.
Equation 7 may, therefore, be written under a form con-
venient for general discussion.
(2=75.04 w. log«. * (9)
The calculus shows that the curve, the area between
which, the asymptote, and two ordinates is proportional to
the logarithm of the extreme abscissa, is an hyperbola,
which is the result reached, page 4.
* For the smokeless powder referred to in Chapter III, p will be prac-
tically = 0, n will diminish, and so will /o for equal values of w. The
effect, as hereafter discussed under Air spacing, will be to make the powder
more progressive ; unless the powder belongs to the class of high explo-
sives and its explosion is of a high order.
XI. — COMBUSTION m A GUN. 1^
Consequently if, as in fig. 5, we assume axes of P and
iV", we may construct various hyperbolas depending upon
the value of w^ such that the areas under them will give^
the corresponding values of Q.
VARIATIONS.
1. In Weight of Charge.
The hyperbolas intersecting at the point P, Fig. 5, and
Equation 7, show the effect upon x,; x' \ x,,; x"; p; n;
Q ; and /, resulting from variations in w.
Inspection of the figure shows that an increase of 7Cf to
7£/ =: -f 7i>, decreases n from about 12 to 7, or about ^ ',
the total length of the bore x' =z x" remaining constant, as in
a muzzle loader.
Owing to the effect on n of variations in w, Q will not in-
crease in direct proportion to w. But, in a given gun, log
n diminishes so much less rapidly than w increases, that we
may for simplicity assume that n is constant; and, taking a
constant ratio between n and x, we may replace the axis of
iV^by that of X, and complete the figure by drawing upon
it combustion curves, as in Fig. 6, so that for the same weight
of charge the areas under the combustion curves are equal,
without regard to the size of grain. See Remark 2, page 7.
2. In Size of Grain.
The curves a' a" , refer to different weights of the same
kind of fine grained powder, which are supposed to be
burned through at about the same point of the bore. Curve
a", refers to a weight w of coarse grained powder.
Consideration of Fig. 6, shows how, by increasing both
the weight of the charge and its inherent progressiveness,
we may obtain a pressure curve, the work area under which
may equal and even exceed that due to the fine grained
powder, without incurring the risk attending the high pressures
to which it gives rise.
14 XT.— COMBUSTION IN A GUN.
In other words, we approach the conditions required in
the ideal gun, by effectively diminishing the value of n.
For, comparing curves a" and b" ^ figure 6, it is evident
that the latter is the more progressive, or more nearly parallel
to the axis of X, and that this results from expansion begin-
ning further down the bore. Neglecting the areas under the
combustion curves, the inclination of which in the diagrams
is purposely exaggerated, the effect is practically the same as
if the powder had been instantaneously burned in a volume,
c -\- c', greater than c, page 2, by the volume through which
the projectile had moved before expansion began. We would
x' p
then have n' =: , , — < n. See Air Spacing,
x, + c'—p
3. In Length of Bore.
While, in all cases in practice, an increase of O m increases
Q and F, the proportionate advantage from the increase of
O m increases with the progressiveness of the powder.
The limit of useful increase of O mis determined by the
intersection of the line of pressures with that of resistances.
Fig. 4.*
In many works on Gunnery the importance of Om^ or the
path traversed by the base of the projectile in the bore of
the gun, is overlooked; or it is left to be inferred from the
total length of the bore.
In the more recent and advanced works it has a specific
symbol u by which it will be hereafter recognized.
AIR SPACING.
Variations in A.
We have so far assumed the powder to be fired in its own
volume. If we assign to the charge a volume greater than
that required to contain it by the volume ^', page 2, the
*This applies to small arms. For heavy cannon the increased weight
of piece resulting from the prolongation of the bore, can generally be
used to better advantage elsewhere.
XI. — COMBUSTION IN A GUN. 15
value of A will diminish. Eq. 8, Chap. IX., shows that the
initial pressure will also diminish, and so, under given con-
ditions will Q. In such a case, Eq. 1, will take the form
/= j — , and the curve expressing the relation
x-\-c-t- c'
p =/ {x) will be such as shown in fig. 7.
Curve 1 expresses, by its ordinates, the varying pressure
when A is large, and curve 2 the same function when A is
small, the weight of the charge being the same in both cases.t
It will be observed that the effect of air spacing is princi-
pally felt when c^ is large, compared with x^ that is, when cs
and/ are relatively large.
Also, since by differentiating Eq. 1, regarding w' as a
df) 11)
constant and x + k=-\^ we have -^ = r-^^; the inclination
aA. Ar
of curve 2, will be less than that of curve 1. The values of
Q and B will therefore both be smaller for curve 2.
Increase of Charge.
If u is fixed, this effect is compensated for, as before, by
increasing w. This produces the effect shown in the dotted
curve, 3, fig. 7.
APPLieATIONS.
Air spacing is principally applied to muzzle-loading can-
non on account of the necessary limit to their length imposed
by the requirements of loading. It results spontaneously from
t To familiarize himself with the principles involved, it is recommended
that the student construct curves 1, 2, 3, as follows :
1. Assume a maximum pressure of say 24 units and<:=l; c^ = o',
10=1; thenfor jr = l,/ = 12; for x=2, / = - =8, and so on.
2. Take c^ =1.-, /& = 2; w=:l, as above; then for x = o,p^=12i
for x = 2fp = Q, and so on.
3. Take^=l and w = 1.5; then for x = o, p=-=18', forjr=l,
/ = 12, as in No. 1; forx = 2, /=9 (greater than No. 1). No. 3 will
continue above No. 1 to oo. The powder is more progressive, and n is
decreased.
16 XI. — COMBUSTION IN A GUN.
the ease with which their projectiles, particularly those
which are spherical, take up their initial motion. It was
probably to diminish this that the sal^of, a cylindrical block
fastened to the rear of spherical projectiles, was formerly
employed, although other reasons are generally assigned for
its use.
Until about 1880, when the EngUsh government began
to adopt exclusively the breech-loading principle for heavy
cannon, air spacing was largely employed for s/wrf, thick
muzzle-\oa,dmg cannon, firing large charges of ^uick-huYn-
ing powder. It was secured by making the diameter of the
chamber greater than that of the bore. This was objec-
tionable in sponging and it weakened the gun.
It was made constant by providing the projectile with
stops, which held it at an invariable distance from the bottom
of the bore. But this, although beneficial in preventing the
great variations in pressure and velocity which, from care-
less loading, are apt to occur in ordinary muzzle-loading
guns, increases the length of the gun in the region of its
greatest diameter.
It is still employed to some extent in breech-loaders, but
is yielding in importance to the means now employed for
regulating the combustion of gunpowder.
EFFECT OF THE ROTATING DEVICE.
If the initial motion of the projectile be restrained by the
compression of the rotating device,/ will have an initial
value at least equal to the resistance offered to deformation,
and, since the powder is burned under higher and more
constant pressures, n will be greater and more constant
than when the projectile is free to move.
ADVAIsTAGtS OF BREEuH-LOADING GUNS.
General Advantages.
1. The simplicity and exactness of the method by which
the value of n may be regulated.
XI. — COMBUSTION IN A GUN. 17
2. The ease with which u may be increased without inter-
fering with the operations of loading.
3. As will be hereafter shown, the compressible pro-
jectiles used in breech-loaders are more accurate than the
loosely fitting projectiles employed in muzzle-loading guns.
In spite of the greater simplicity of construction and of
operation of muzzle loaders, these advantages have com-
pelled the adoption of breech-loading cannon.
Tactical Advantages.
The tactical advantages of breech-loaders are also greater.
Among these are —
1. Greater facility in securing cover for the piece behind
defenses, and for the gunners behind the piece.
2. Less danger and difficulty in loading, since but one
charge can be inserted at a time, and the operation of spong-
ing is less important than with muzzle loaders.
3. Greater facility in examining and caring for the bore.
4. Greater facility in adjusting the charge or fuze after
loading.
5. ImmovabiUty of the projectile in marching. This per-
mits batteries to come into action rapidly, when under fire.
6. The rapidity of fire is increased for large pieces.
The price paid for these advantages is the difficulty of
getting officers and men capable of working the cannon with
sufficient care.
OBJECTIONS TO INCREASING WEIGHT OF
POWDER.
The preceding discussions show that we compensate for
small values of 7i by corresponding increases in the value of w.
The objections to this are as follows.
1. We increase the waste of powder, as the steam en-
gineer does that of his coal by failing to work his steam ex-
pansively. This may be of importance when storage capacity
is limited, as on ships and in the field, and it tends to dimin-
ish the value of ?y, hereafter explained.
18 XI. — COMBUSTION IN A GUN.
2. The work done in distributing the gas throughout the
bore increases with the weight of the charge and the length of
u. Some charges now weigh half as much as the projectile.
3. We increase the tension of the gases within the gun at
the instant of the departure of the projectile. This tends
to accelerate the recoil and to perturb the flight of the pro-
jectile ; since, owing to their small mass, the gases leave the
gun with a higher velocity than that of the projectile.
4. Considering the gun to consist of a number of staves,
like those of a barrel, the moment of the pressures about the
breach is increased on account of their greater level arm.
5. Variations in / and «, due to accidental variations in
the velocity of combustion, may endanger the safety of the
piece or affect its accuracy.
IGNITION AND INFLAMMATION IN GUNS.
The importance of these phenomena has largely decreased
with the adoption of the breech-loading principle.
When muzzle-loading cannon, firing free projectiles with
charges of fine grained angular powder were generally used,
.1 . . time of inflammation ,
the ratio -— ^ , — was large.
total time of conversion
To reduce this as much as possible, so as to increase the
value of n^ the charge was ignited near its middle. It was
found that ignition in rear tended to waste energy by moving
the forward portions of the unburned charge ; while that in
front reduced the velocity by the premature movement of the
projectile.
With breech-loaders the charge is always inflamed before
the projectile has moved.
The shape and size of the grain and the use of a special
priming of quick powder placed near the vent, reduce the value
of the ratio of times above referred to so much, that the
position of the vent is determined by other considerations.
XI. — COMBUSTION IN A GUN. 19
MEASURES DEPENDING UPON THE MUZZLE
ENERGY OF THE PROJECTILE.
1. MILDNESS OR PROGRESSIVENESS.
P =: / TT r^ is called the variable total pressure.
In this, and in subsequent similar expressions, r is expressed
in the same linear units as those of the area upon which / is
estimated.
When/ has its maximum value, as indicated by the pres-
sure gauge, and taken = /„ ; the maximum total pressure is
P' = x' p', Fig. 8.
The area under the pressure curve divided by u gives the
mean total pressure P,-=^ — = m p,.
u
The effective length ox u' = — = O x".
Therefore, if we represent the following ratio by ju, we
have, since E = P' u' = P, u,
^ = ^^'!L^^^ ^^' . (10)
^ P' u P' u ^gp.-ar'u
in which /^ and JVare expressed in the same units, and g, u
and Fin the same units.
This coefficient /x, which measures the ratio of the area
under the curve to that of the circumscribed rectangle, may
be taken as the measure of the mildness or progressiveness
of the action of the gunpowder under the circumstances of
any particular case.
The limit of the ratio for all ordinary powders is evidently
unity, and would be reached only in the ideal gun.
2. ECONOMY.
-p
7) = — is a valuable datum for comparing the economy or
w
efficiency of various powders.
^0 XI. — COMBUSTION IN A GtjM.
It appears from figure 3 that the greater is the efficiency,
the greater is the maximum pressure ; or that the violence of
gunpowder increases with rj. Also from figure 2, that the
smaller the value of r, or the quicker is the gunpowder in a
given gun, the larger will be the value of t].
It would be more consistent to follow the method adopted
for jLt, the value of which is independent of any particular
metrical system \ but in order to avoid dealing with large
numbers, and because of the general use of the term " foot-
tons of energy per pound of powder," we shall write
3. GENERAL COEFFICIENT.
The preceding discussions show that all expedients intended
to increase the progressiveness of powder decrease the muzzle
energy resulting from the conversion of a given weight of the
explosive ; or decrease rj.
Thus, when, as in figure 3, we increase the size of the grain,
or vary its form, composition or density so as to increase r ;
or when, as in figure 7, we diminish /^ by decreasing A, we
decrease the Factor of Effect ; and therefore, in order to ob-
tain the muzzle energy required, we must increase the weight
of the charge, as shown in figure 6.
In order to compare the performance of different powders
fired under the same conditions, or of the same powder fired
under different conditions, it is proposed to use a general co-
efficienty known as x '• which, since fi and r] are both desir-
able, will be proportional to their product ; and which, since
they tend to vary inversely with each other, will have an
approximately constant value.
This relation may be expressed by writing
X-iin= ^^mp.TTiP uw' ('^^
XI. — Oo^rBusTloW in a gun. 61
It will be hereafter more fully discussed.
4. STRENGTH OF GUN CONSTRUCTION.
// = -j^ , in which IV' is the weight of the gun (in the
same units in which IV, the weight of the projectile, is expres-
sed) measures the height through which the gun would have to
fall in vacuo to acquire energy equal to that residing in the
projectile at the muzzle of the piece.
Thus the old 10 in. S. B. C. I. gun had a value of ^ = 300
ft. When strengthened by a rifled steel tube that reduces its
caliber to 8 in. we have the "converted" 8 in. Rifle, for which
A is about 350 ft.
For the new 8 in. B. L. R. Sfee/, h is nearly 500 ft.
6. FACTOR OF EFFECT.
The meaning and derivation of this have already been
explained.
Use.
It is used for anticipating the effect of changes in the
interior form of a piece, or in its ammunition, upon the
muzzle energy of the projectile.
It differs from the use of x ^"^ its factors in taking no
heed of the maximum pressure involved in the result.
Conditions.
It is necessarily assumed to remain constant during the
variations, the effect of which is sought; and consequently,
the conditions under which it is employed should be as
nearly alike as circumstances will allow.
These conditions relate to the type of gun, of powder,
and of projectile employed •
Owing to the greater constancy of A, and to the high
initial pressure required to move the projectile from its
seat, it is better adapted for use with breech-loading than
with muzzle-loading cannon.
M. L. R.
B. L. R.
30
60
50 1
65
75
^ 80-85
85
22 XI. — COMBUSTION IN A GUN.
The factor of effect increases with the size of the gun, as
seen by the following table, giving its approximate value,
in certain individual cases. So much depends upon the kind
of powder used that only the most general conclusion can
be drawn:
Factor of Effect Per Cent.
Muskets,
Mountain Guns,
Field "
Medium "
Heavy "
APPLICATIONS.
1. Variations in w and a .
1. Suppose it be desired to estimate the change in the
muzzle velocity to be expected in a given gun from certain
charges in a/ or A.
The values of E and Q, under known conditions, have
been determined; and therefore,
F= -yr is known.
Determining, from Eq. (7), Q' under the new conditions,
we have-£''=i^ Q'. On firing we should find approximately —
V=JJEl^. (13)
2. Untried Gun.
2. Suppose that we desire to estimate the muzzle velocity
of a given projectile to be fired from a new and untried gun,
of which we have only the drawings.
We select the record of some gun of as nearly the same
type as possible, assume F=F\ and proceed as before.
3. Dimensions of Guns.
3. The inverse problem may also arise; viz., to determine
the interior dimensions of a gun of any required power.
XI. — COMBUSTION IN A GUN. 23
Eq. (7) may be placed under the form —
w
Q=l!6Mwlog (l4)
^,-23.9,-^
The calibre and the density of loading, A, are always
assumed, the former depending upon the service, and the
latter upon the strength of the gup; therefore, since
27.68 w
A =
V=7C — X,,
110.72 «; (15)
' TT ^2 A
We have, therefore, two problems:
1. Assuming u to find the necessary values of w and x^,
2. Assuming iv to find u.
The difficulty of simplifying an expression of the form
of Eq. (14) requires these solutions to be made by trial.
In the first case, taking F from some similar gun, we have
01 =■ —=r- Then, assuming successive values of w, we insert
them and the corresponding values of x^, determined from
Eq. (15) into Eq. (14) until a suitable value of Q^ is obtained.
In the second case, we proceed as before, substituting
successive values of u.
The initial approximations to the value of u will be facili-
tated by reference to the value of n, usual in guns of the
type proposed.
EXAMPLES FOR PRACTICE.
1. The 3.20 B. L. W. I. Chambered Rifle, in which x,^
12 in.; u= 56.1 in.; 3 lbs. I. K. powder = ze/, gave to a I'Z
lb. projectile, F= 1548/.^.
^4 XI. — COMBUSTION IN A GUN.
Determine its factor of effect;
j,_ E _ 199.3 _
2. Estimate V for a 13 lb. projectile to be fired from
the new 3.20 B. L, Steel Chambered Rifle with a charge of
3.75 lbs. I. K. powder.
From the drawings we find that the volume of the cham-
ber, which is a truncated ellipsoid terminated by various
cylindrical and conical surfaces, when diminished by the
volume of that portion of the projectile which lies within it,
= 123.157 cubic in. Similarly, the length of the rifled por-
tion of the bore, when increased by that of the projectile
lying within the chamber,^ 73.24 in. Therefore, ^^= 15.31
in., x' = 88.55 in; and in the case supposed n = about 12 as
before.
We find (2' = 303.9 ft.-tons, ^=247.4 ft.-tons, and
F=1657/.J.
By experiment, F= 1662 f.s.
The difference falls within that usually found when all
the conditions are as nearly constant as possible.
DISCUSSION OF THE COEFFICIENT X.
A study of many records shows that when the conditions
of loading approach those sanctioned by experience, the
value of X expressed in the units assumed varies from about
24.0, when the powder is so quick* with relation to the gun in
which it is to be used, that the weight of the powder is only
about one quarter the weight of the projectile ; to about 35.0,
when the powder is so slow that 7a may be safely increased
to about one half the weight of the projectile.
* The remark on page 6 shows that the same powder may be quick in
some guns and slow in others. Thus the powder suitable for a field
piece would be too slow for a musket, and too quick for a siege piece;
and in two siege pieces of the same caliber, this powder would be quicker
in a gun, than in a howitzer or mortar.
XI. — COMBUSTION IN A GUN. 25
It is rare to find a value of x ^vith any form of black pow-
der greater than 28.0; while with cocoa powder it often
approaches 35.0. Furthermore, these values approach con-
stancy, as will be seen from the table on following page.
The approximate constancy of x enables conclusions to be
drawn from otherwise perplexing data. Thus, in the 7.0 in.
Howitzer in Table I., it might be difficult to decide which
was the better powder, L. X. B. or I.. K. K.; but the values
of X show that the former is to be preferred.
If we assume axes of ?/ and fj, as in fig. 9, we may refer to
them as asymptotes certain hyperbolas which will limit all
reciprocal values of rj and ^ for each kind of powder. Thus
powder /^, for any assigned value of 7] or fi will give a higher
value of [J, OT rj than powder a.
0( the two principal ballistic data, viz.: Fand /„, the
former is much more easily and certainly obtained than the
latter. Indeed, unless the pressure gauges are carefully pre-
pared by experienced observers, their indications are fre-
quently mconsistent.
Therefore, a known value of x ^'^^Y be employed to check
the records of the pressure gauges, or to replace them; for,
having observed V, we have
^" ;^ 2240 ^^77^/^ 7/ ^ ^
Also, having ascertained by experiment the value of \i^ or of
7\ for any powder of which we know the coefficient x^ ^^^ may
estimate the weight of the charge of that powder required to
give to a projectile of any desired weight the maximum
velocity which the limit of pressure imposed by the construc-
tion of the piece permits, or
The density of loading will be regulated by this value oi p^.
As will be shown in Chapter XII., the value of X-, for the
26
XI. — COMBUSTION IN A OUN.
Sphere Hex'l powder.
Converted gun.
Steel gun.
Flat powder.
Black Prism.
Hexagonal.
Reported "good."
Reported "good."
Rep. "entirely too quick"
Rep. "entirely too slow."
^
'^o:rrt-iM<Ma:QOOor'Cooscoco(MTrioocc<M
(M (M CI C-l (M <M C^l (M (M Ol (M (M (M (M fM CO CO CO CO
5r
OiO(M-«^iCOQ00iOt^OC00i0i»r5i0.«OO
oooi-ioooitooiCiTt^inTfmt^co'oicot^TtiQO
a_
<
i-HOOOt-OOOiOOOOOiOOC<IO-<fCO
'X)ooiOin)0?oor-oooo(Mio<x>OTj<T(i
(Mt-kOOOOOS-^OO-VOiC^rHCDCDlOOOtD
tooDOoso^-rjiascoiooocooot-fMeoocooo
(M(MCO(MCOC0CCC0COr-i(M(M(MCqcOC0COC0<M
^
t-OCCOOOiOiOOlOCOt'tftOSOOiOT-Ht-CO
«OrHCOC0C0Tf<(MtOtOTtiO5(MQ0C0<X)<MC0C0C0
PL.
icooooooooio»a»rsicoo
ocoeocoincocotoioooooocoosososr-i
rH ri C^l (M (M CO
pi
g
9
COOOlOOOOOOOCTOt-'
lo ift ift in o o
lOCOCOCOCOCOfMiflTtitDOiOSOSCOTfOOOr-l
: : i : : i^'.i : i ! : : i : :** ; ;
M w w w w >< ^ 'i ^ >< >< ^ wV >^ izi ^' <i p=3
vj k4 fj KH* w h4 c» S 6 J J J J h k cu d>Q^ d»
S
3
urj in u'. o o CO o lo »o o
COOOCOCOCOCO-^TtiTtiOOOOrM(M''<!lHTj<-<:j3TlJ
(M ^ (M (M (M (M ^ (M (M -< — r-H r^ — -*(?} (M -M (M
8
ITS lO iQ O
lft-X)(M(M(M(MOOQOOOQOOOCOOOOOt-t-C-l>
■^tOCOCOCOCOOSOSOCOCOCOCOCDOlOlClOlO
'«.S
coeococococoidu^int-^r^iT-t^ooQOGdGOOOGO
^
3
XI. — COMBUSTION IN A GUN. 27
same powder fired in the same gun, will increase as the ratio
— mcreases ; but a nearly constant expression called 11 will
result from multiplying the computed value oi xhy j — j ^ or
\ W / /„ a u wl
log 6^=6:2161.
By comparing different values of IT, we may compare the
performance of different powders in the same gun, even when
fired with different charges, provided the weight of the pro-
jectile is constant, which is usually the case.*
THEORY OF COCOA POWDER.
The facts that, although almost all possible combinations
of the ingredients of ordinary black powder have at different
times been tried without decided advantage over those gen-
erally adopted; and that, as we have seen, the changes in
manufacture which have had as their object an increase in \i
have necessarily correspondingly reduced ?/, indicate that the
difference in the action on the brown powder is due to some
marked difference in the chemical composition of its charcoal.
This was for some time a secret for which it is said that the
British Government paid a large sum. Without requiring
such payment, the Messrs. Du Pont, of Wilmington, Dela-
ware, the manufacturers of a powder that has shown itself to
be nearly equal to that made abroad, have furnished the basis
of the following theory as to its peculiar behavior.
* So many of the records require the value of u to be assumed from the
proportions of the gun, and so doubtful is the accuracy of many of the
pressures recorded before the theory of the pressure gauge was well
understood, that the constancy of x ^o"" ^ given gun and powder is best
seen from an analytical discussion in Chapter XII. The table is given
rather for illustration tha\. for proqf.
28 XI. — COMBUSTION IN A GUN.
The charcoal made by superheated steam contains a large
proportion of free hydrogen and much more in relatively
unstable combination.
The carbo-hydrates^ as are termed the resin, gum and
sugar added during manufacture, are also magazines of
hydrogen.
The effect upon the velocity of combustion, due to the
presence of the gum and to the high density of the powder,
and possibly also some of the phenomena of dissociation
under high pressures, prevent the sudden liberation of the
hydrogen and its combustion when x^ Eq. (1), is small.
The hydrogen combines as the pressure wanes, and tends
to sustain the pressure and to increase both 7\ and //, whereas
in black powder they must vary inversely.
The water formed serves to precipitate the smoke, the solid
particles of which are entangled in a condensed spray of
liquid gum following the projectile.
To this may be added, as a theory more generally accepted,
that the large proportion of nitre tends to prevent the forma-
tion of CO, thus reducing the volume of the gases first formed,
and diminishing the violence of their action, or increasing \ji„
On the other hand, the excess of nitre may tend to increase
7\ on account of the more perfect combustion of the charcoal
and the high calorific value of the hydrogen which it contains.
The precautions usual in manufacture are taken to affect the
size, shape and density of the grain and the amount of moist-
ure it contains, so as to increase its progressiveness.
That these precautions alone do not account for its peculi-
arities appears from the fact, that while a prism of black
powder burns in the open air in \\ seconds, and a similar
prism of brown powder burns in 10 seconds, equal charges
of the brown powder give equal or higher muzzle energies
than the black powder without exceeding their maximum
pressures.
XI. — COMBUSTION IN A GUN. 29
English Experiments of 1890.
1'hese furnish the following data from which the effects of
the composition of the powder may be observed.
SoHd residue per cent :
Permanent gases per cent of volume :
7\ oi permanent gases above
Heat units per kilogramme
/= v^ H. (Chap. IX, page 7) ratio
Specific volumes of water vapor
Black.
Brown.
K.CO,
m
64
Kir CO,
—
14
s
9
—
K,S
15
—
KSO,
10
22
iim(3 •
100
100
UIIlC .
CO,
47
51
CO
16
3
H,S
3
—
ZTand CH^
4
4
N
30
42
100
100
278
198
721
837
•atio
1.0
0.83
41
122
XII. — SARRAU S FORMULAE FOR INTERIOR BALLISTICS.
CHAPTER XII.
SARRAU'S FORMULAE FOR INTERIOR
BALLISTICS.
The deductions of M. Emil Sarrau permit a very accu-
rate solution of many important problems affecting the
interior form and the method of loading cannon.
By methods which are too elaborate for present instruc-
tion, Sarrau deduces four general formulae for pressures
and velocities.
Notation.
The units in the following notation are based upon those
adopted in the publications of the Ordnance Department,
U. S. A. Some changes are made in the notation to make
it agree with that previously used in this work. Where
Sarrau's notation differs, it is given in brackets.
Let
V. (v) Muzzle velocity, in feet per second,
/o (F^ Maximum pressure on bottom of bore in pounds
per square inch.
/ {P) Same on base of projectile.
d. (c) Caliber in inches.
u. Length of the travel of the base of the projectile in
the bore, in inches. See Chapter XI, page 13.
W (/) Weight of projectile in pounds.
w {n) Same of powder.
A Density of loading.
d Specific gravity of the powder.
N' The granulation of the powder, or the number of
grains per pound.
2 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS.
/ Force of powder when A = 1, Chapter II, page 7.
r Time of combustion of a single grain, referred to a
standard grain as unity. See page 5.
S Initial volume in cubic inches; the same as F,Chap-
ter IX, foot page 3. This volume generally
differs from the capacity of the powder chamber
since the base of the projectile may occupy some
of this space.
8 The reduced length of the initial air space which is
equal to v' (Chapter IX, page 3) + ^' (Chap-
ter XI, page 2).
We have z=S — v. but
4 '
e 27.68 7£/ , 27.68 7£/ ,, .
o.= and z^,= : therefore
A
110.72 w
(i4)
a and / (Sarrau uses \ instead of /).
These are two numerical coefficients depending on
the form of the grain, which are functions of the
ratio of the least dimension of the grain to its
other dimensions. See page 3.
a and fi. Two very important characteristics depending
on the nature of the powder; viz, both on its form
and the time of its combustion. Their values are
obtained from the following equations :
m
^= r (3)
Owing to their preponderating effect in the prin-
cipal equations which follow, a is known as the
XII. — SARRAU'S FORMULif: FOR INTERIOR BALLISTICS. 3
pressure characteristic^ aod p as the velocity char^
acteristic.
A, B, M, K. Certain empirical constants to be determined
by experiment.
Form of Grain.
If we develop Equation 5, Chapter X, according to the
ascending powers of — the development may be placed
under the general form *
j=/w=<.i(i_/i+«i;+&c. . . . .) (4)
This may be shown to apply to other forms of grain
besides the sphere, the coefficients of — varying with the
form of the grain and by their values characterizing the
mode of combustion in so far as it is affected by the form
of grain.
I. For spherical grains it readily appears that
a; = 3; /= 1; m = Yi,
The coefficient m is neglected as insignificant.
Besides the spherical grain, which includes not only true
spheres, but grains the form of which approaches that of a
sphere, such as cubes, hexagonal powders and those of
irregular granulation ; powders are classified as to form, as
parallelopipedons and pierced cylinders. Both classes in-
clude the forms most closely resembling the type, e. g. L. X.
powder would belong to the former, and pierced prismatic
powder to the second class.
* In the above equation replace — by jr, then
f {t) =z\— {X — x)^ =^^ X — 2, x" ■\- x^
= 3-(i — + -') = T [1-7+1(7)']
For grains of other forms a similar but more extended method is followed.
4 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS.
II. For the parallelopipedon, if x and j^ represent the ratios
of the least dimension of the grain to its other two dimensions
the development of the corresponding function of — will give
T
the following characteristic values for the coefficients a and /,
a
If the base of the grain be square, x — y^ and
a=.\-\-%x; I— ••
a
III. For the pierced cylinder, x represents the ratio of the
thickness of the walls of the cylinder to its height, or con-
versely; the lesser dimension being divided by the greater
in either case. The cylinder is supposed to burn all over
at once. The following are the values of the coefficients
for the pierced cylinder described:
a=:l-{-xj 1= -.
a
Since the ratio x has generally given to it a value of J
we may form the following table.
TABLE I.
Values of ^
Form of Grain. a I
I. Cubical; Spherical; Hexagonal;
Irregular granulation 3.0 1.0 3.0
II. Parallelopipedon ; flat powder 2.0 g 3.2
III. Pierced prism or cylinder, one hole f J 4.5
By substituting these values of a and / in Eq. (4) we may
represent graphically, as in figure 1, the variations in the
rate —=^o for grains of equal weight but of different forms,
burning in the same time t.
XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS.
If the rate of conversion is uniform, Eq. (4) becomes
t
f {t)-=.a- and /, /? and y (post) reduce to 0.
T
Size of Grain.
The mean diameter of irregular grains results from know-
ing their specific gravity and granulation as follows*
/6x27.68\i / 52.86 \1
For powders of regular granulation a similar method may
be preferred to the actual measurement of their dimensions.
VELOCITY FORMULA.
Monomial formula for quick powders
'=Ma (i)
Binomial formula for slow powders
(A)
in which
F=Aa(wu)^^-^y[l-rl (B)
The choice of the formula to be employed in any case
depends upon the value of y. With a given gun and pro-
jectile this depends upon the value of /3 and therefore,
under the conditions of loading, /3 measures the quickness
of the powder.
The form of the function y shows that its value depends
largely upon the gun as well as upon the powder. Conse-
*Ca\\v=s -—the volume of the mean grain, the weight of which in
pounds is w : then
^vze;-i 27.68- '^^vrd^.
6 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS.
qiiently the same powder may be quick in some guns and
slow in others. Chap. XI., p. 24.
When y > 0.273, Equation (A), should be employed, and
conversely for Equation (B). The two equations give but
little difference in results when the conditions make y
approach 0.273.
Referring to the value of /?, Equation (3), it appears
that the value of y cannot be known until r has been deter-
mined. It is evident that the methods described in Chapter
VIII are not sufficiently accurate, so that the following
practical method is adopted.
Determination of Constants.
A well defined molded powder is taken as a standard and
its values of / and r accepted as unity. For this powder
the values of a and (i, Equations (2, 3), reduce to y a and /,
which can be measured by the means described, page 3.
To determine the value of M in equation (A) we substi-
tute the value of F obtained as the mean of several fires in
a gun in which the standard powder is relatively quick, and
solve with respect to M.
In equation (B) we proceed similarly for A and B, select-
ing two very dissimilar guns and taking their conditions of
loading so as to cover as wide a difference of limits as is likely
to occur in practice.
Choice of Formula.
Inasmuch as the values of A^ B, J/, are true for all
powders, and since (Chapter IX, page 6) the force of all
nitrate powders may be taken as constant, and in this case
equal to unity, equation (A) may be written
--(0'(v)-
S 1 ,1 8
and placing
M^^^ = X (7)
Xll. — {JARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 7
we obtain
r = «*/-3X«. (8)
If this value of r substituted in that of y, Equation (6), makes
'y> 0.273, Equation (A) may be used; but if it makes y<
0.273, Equation (B) must be employed.
To determine the true value of t for use in Equation (B)
requires a method of approximation which .s too long to be
given here, but can be found in the works mentioned in the
bibliography. This will not generally be necessary, as the
characteristics may be determined directly, as hereafter ex-
plained.
The value of r for the standard powder is approximately
equal to the time of its burning in air at the rate of about
0.4 inch (1 decimeter) per second. Other values of r will
therefore have approximately their values in air.
Rejnark. — The first term in liquation (B) represents the
ideal case in which the form of the grain is such that the
rate of conversion (Note, foot page 2, Chapter X.,) is uni-
form. The second term is sub tractive and represents the
effect of the decrease of the rate of conversion, or of the
burning surface, when the grains have the forms required in
practice. It is evidently an advantage to have the second
term as small as possible.
Empirical Constants.
The numerical values of A^ B, M^ the determination of
which has been incidentally described, depend only upon
the units of measure adopted for dimensions and masses.
In the Ordnance Department, the units being respectively
the inch, for internal dimensions of guns; the foot, for
velocities per second, and the pound, the constants have
the following values given by their logarithms :
log A = 2.56635 ; log ^= 2.80964; log M= 2.84571.
The other terms in the formula require no change ; since
the effect of changes in the units by which the different
8 XII. — SARRAU's FORMULA FOR INTERIOR BALLISTICS.
elements of loading are measured, is compensated for by the
numerical value of the empirical constants.
PRESSURE FORMULA.
The following equations are employed to determine the
pressures on the base of the projectile and on the base of
the bore.
p=Ka^£u ( Ww)^d-\ (Q
in which log ^=3.96198.
/o=^o «' A W^ wU-^, (P)
in which log ^o=4.25092.
Equation (C) is obtained by differentiating the equation
for velocity and determining the maximum acceleration of
the projectile; it can be verified only by the apparatus
described Chapter VII. But equation (D) can easily be
verified by the pressure gauge. See Chapter XI, pp. 8 — 9
PRESSURE CURVES.
In designing guns it is indispensable to know something
about the pressure at other points along the bore than that
at which the maximum pressure occurs.
In Chapter IX we have considered an approximate solu-
tion; but Sarrau's formula furnishes us a method which is
much more accurate.
Expansion Curve.
If in equation (B) we call
J,=Aaw^\^-jP^j f (9)
M.=BJ3^^> (10)
For the same gun, conditions of loading and powder,
equation (B), becomes by writing, v, the velocity at any
XII. SARRAU'S FORMUL/E FOR INTERIOR BALLISTICS. 9
point of the bore, for F, the muzzle velocity, and calling u
the variable length of travel of the projectile.
v^A^u\{\-B^u\). (11)
If we differentiate equation (11) with respect to v and u^
and divide by dt^ we have
^ = (|^,«-|-J/(,^,«-j)^ =/(«)$. (12)
in which -y- = v and -^ = acceleration of the projectile, or
at at
dv i) 7T d^ <""
calling/, the variable pressure on the projectile ; —=<-L- ^,
From this follows
Combustion Curve.
It is not recommended to depend upon the values of /,
u
thus deduced for a travel of the projectile of less than ^ ;
because the velocity formula is not considered reliable for
such small values of u as those existing during the com-
bustion period. Chapter XI page 1.
The form of the pressure curve in the initial portion may
be determined as follows.
It appears from the following table based upon the analy-
sis of Sarrau that the displacement of the projectile corre-
sponding to the maximum pressure, or C/", is equal to 0.6 Zy
equation (1). This gives us the locus of this pressure and
equation (C) gives us the intensity. It remains then to find
the form of the portions of the curve in the neighborhood
of the point of maximum pressure. This is obtained from
the following table which gives the proportion of the
maximum pressure exerted at points near the displacement,
Uj above. In this table the variable jo represents the ratio
10 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS.
u d"^ y • •
_, and — v^ values proportional to the acceleration, since
z dx^
X, in this case represents a certain function of /. It has no
connection with the quantity x, on page 3.
TABLE II.
^0
y^
JVo
d^y.
dx^
0.1
0.180
0.6
0.710
1.25
0.651
.3
.605
.7
.705
1.50
.621
.8
.665
.8
.700
1.75
.590
.4
.693
.9
.692
2.00
.563
.5
.700
1.0
.680
2.50
.513
That is to say that after the projectile has travelled over
a distance equal to the reduced length of the initial air space,
the pressure is -||- of the maximum; etc.
It is supposed that the pressure on the wall adjacent to
the base of the projectile is to that upon the base, as 10 is
to 7; so that by multiplying the pressures just determined
by 1.43 it is easy to determine the probable intensity of
the corresponding pressure on the walls of the bore.
QUICKNESS OF POWDER.
Sarrau has established for powders fired under various
conditions of loading certain moduli of quickness which
express their relative quickness under these conditions.
See page 5.
The modulus of a powder forms an important independ-
ent characteristic which is of considerable help in establish-
ing auxiliary equations of condition for the solution of
problems in Interior Ballistics.
It may be shown from equation (B) that if, among the
variables in the second member, r alone be caused to vary,
the function, F, will pass through a maximum state.
XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 11
In practice this is not absolutely true ; for, as already
stated in Chapter XI, the smaller the time of combustion,
the greater the number of volumes of expansion in a given
gun, and hence the greater the kinetic energy due to a
given charge.
Equation (B) is derived by a process of approximation,
and its physical significance cannot therefore be rigorously
interpreted. It serves to show, however, that there is a
limit below which the reduction in r has but a very slight
effect upon the velocity, and which it is inadvisable to pass;
because, as r diminishes past a certain point, the velocity
increases very slowly; but the maximum pressure very
rapidly.
The value of r corresponding to the maximum value of
Fis obtained by placing equal to zero the first differential
coefficient of the second member of equation (B) regarded
as a function of r and solving with respect to r.*
Denoting this value of r which is called the time of the
maximum (velocity?) by Tj we have
r. = 3^((^. (14)
a
In a given piece a powder behaves as a slow powder
when the time of its combustion, r, is notably greater than
* Equation B may be written,
V=C\p{t)=^CiT-\ — RT-\\
in which
.=.£(i^ c=. (/«)»(.„)» (A);
Hence
— =C(— ^r 2-\-\Rt 2)
by placing —- =0.
a T
r,=.S^^SJ^'JKpl
(U)
12 XII. — SARRAU'S FORMULi*: FOR INTERIOR BALLISTICS.
that which in the particular arm corresponds to the theoret-
ical maximum of velocity. Further, two powders fired in
different pieces should be considered as equivalent as far as
regards quickness if their times of combustion are propor-
tional to the times of the maximum for the two pieces
employed. Consequently we may call the ratio
^ = ^ (15)
the modulus of quickness under the particular circumstances
under which the powder is fired ; since the more nearly does
Tj equal t, the more nearly does q approach unity.*
Under this view we may adopt the following arbitrary scale
for the classification of powders :
TABLE
III.
Value of Modulus.
Nature of Powder,
1.0
Very quick.
.9
Quick.
.8
Medium.
.7
Slow.
.6
Very slow.
Since the above classification was proposed by Sarrau, it has been
found advisable to extend the value of the modulus in both directions.
For long Sea Coast guns it now runs as low as 0.4, while it has been
found advantageous in the B.L. mortars to increase it to 1.3.
In any case we have
(W u)^
q=^Bp^—^=dy. (16)
VELOCITY AS A FUNCTION OF THE MODULUS.
By introducing q in place of r in equation (B) we may
obtain a new and useful monomial equation of the general
form
* The modulus of quickness also is designated by Sarrau as x.
XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS.
13
V=^A^,B)-^(l{y±^^ (17)
in which /(^) may be taken as Nq^\ N being some con-
stant.* See page 28.
Collecting the different empirical constants under one
head, which we may call M, and ascertaining that for the
particular form of / (q) employed we have
n = i^fZ^.; (18)
we find that equation (17) reduces to
In equation (A') V varies with n\ that is, with the
modulus, ^, upon which by equation (18), n depends. It may
be used as an approximation, as on page 6, by giving to 7t a
constant value under conditions of loading which are such
that the modulus is comprised within certain limits.
*This equation shows that under given conditions of loading the initial
//a\\
velocity is proportional to I -y I .
This factor is called the ballistic coefficient. It depends both upon the
force of the powder and the form of the grain. If the force be considered
constant, the ballistic coefficient depends only on the form of the grain.
By transforming Equations ( 2, 3) we have
^ -T-J'
It will be observed from Equations (C^), (D^), that the pressure varies
with the square of the ballistic coefficient. This relation imposes a prac-
tical limit to increasing the velocity by the increase of this coefficient.
The ballistic coefficient of the powder must be carefully distinguished
from the ballistic coefficient of the projectile to be hereafter discussed.
14 XII. — SARRAU*S FORMUL.*^ FoR tJJtERlOR BALLISTICS.
It is convenient to remember that n increases as q de-
creases: when ^=i\-, ^=-J; and when ^=3^, n:=\*
It is considered that these are the limits imposed by
practically satisfactory conditions of loading. See page 21.
By making q—^ equation (A') reduces to the form of
equation (A), which was thus derived.
Since q—'6y and since the value of q=^ is taken to be
about the highest modulus that can be profitably employed,
we see why the maximum value of y on page 5, has
been determined =3^-^-3=0.273.*
MAXIMUM PRESSURE AS A FUNCTION OF THE MODULUS.
By substituting for - in the value of a', equation (C), its
value — derived from equation (14), Sarrau finds
^=^(3^)-^^^(v)^. (C)
and similarly
A = ^o(3^r -/-(»^) ^(v) i- («)
PRINCIPLE OF SIMILITUDE.
Two guns are similar when all their homologous linear
dimensions are proportional to their calibers. Chapter
XVI, page 17.
The similitude is extended to the loading when the
weights of the powder and of the projectile are proportional
to the cube of the calibers, and when the grains of powder
have the same form, composition, density, etc., and their
^Although not so named, it is convenient to think of n as the modulus
of slowness.
Xlt. — §ARRAU*S FORMULife fOR iNtEklofe 6aLUSTICS. 15
dimensions are proportional to the calibers. Consequently
the numerical coefficients a^ /, must have the same values,
and the value of r must vary proportionately with the caliber.
The principle of similitude enables the following proposi-
tion to be proved, viz. :
In similar gims, similarly loaded^ the velocities and pressures
corresponding to distances passed over, which^ measured ifi cali-
bers, are equal, are respectively equal to each other.
For, let us consider two guns having calibers respectively
equal to d and to d' such that d' z:^ B d, and substitute in
d'
Eq. (16), (17), the ratio d z= — raised to powers varying with
d
the quantity considered, as follows :
From the conditions of similitude we have
w:w' :: W: w^':: d^ : d'\
or
7e> - W ~ \ d ) —^ '
u' d'
and Ji = 4_ = 6>.
u d
In Eq. (17) the factors A, B, A, N, and the ballistic co-
efficient will be eliminated by division, so that substituting
for — |- , (03)i = $1 and so on, we have
I q' r
Similarly in Eq. (16) since /? =r --, zr — j Q.
T \ q'
Now if T varies with the caliber, —j- = —^, and — = 1,
T ~"6I
or V= V,
Since the muzzle may be taken at any distance the propo-
sition is proved as to velocities and can be shown to be true
as to pressures by the similar treatment of Equation (C).
16 XII. — SARRAU'S FORMUL.^ FOR INTERIOR BALLISTICS.
But if the same powder is used in two similar guns of
r V d'^
different caliber — r- = 1 and -yit- = (QY = -7—.
t' V d^
Consequently, for the same powder in similar guns, the ve-
locity varies as the ^z**^ power of the caliber.
Equation (D) similarly shows that when the same powder
is used in similar guns the pressure varies as the caliber.
This is a more exact explanation of the practice of vary-
ing the size of the grain to suit the gun than that given
Chapter XI, page 7.
INFLUENCE OF THE CONDITIONS OF LOADING
UPON VELOCITIES AND PRESSURES.
General Statement.
Let us consider as constant for any gun the quantities d^
u, IV, and as constant for any powder its force and form of
grain, or/, a and /, i.e., its ballistic coefficient.
The quantities which may then be varied so as to affect
the velocities and pressures are w, A and r.
There are an infinite number of sets of values of these
variables which will give the same velocity with different
maximum pressures, or the same pressure with different
velocities. The pressures considered are those upon the
breech of the gun.
The following practical rules result from differentiating
the Napierian logarithms of the above named variables in
Equations (17) and (D'). In equation (17) the differential
of the Napierian logarithm of the function of ^ which it
XII. — SARRAU'S FORMULi^: FOR INTERIOR BALLISTICS. 17
contains can be shown to reduce to the form *
'^l0ge/(?)=-«^, (19)
and in equation D',
d\oz,q= -—-; (80)
therefore
d V dw d b. dr
dpo dw d l\ d t
po ~^ w "^ A ~r
(21)
(22)
These equations enable us to determine the variations
in velocity and pressure corresponding to very small incre-
ments of the variables w, A and r.
The influence of each variable on the value of the velocity
and pressure is measured by the coefficient which multiplies
the relative variation of each variable in the above equations.
In Equation 21 the coefficients of , , and are
respectively § ; \\ n = ^ S^T^ '
bince a = — ; a^ = == — (/ —
^ r T T T
dq dr
Also d log. f (q) = d loge N q-=J-S^L^
A/ q'^
d q^ n q^~^ dq
d T
=.11 d loge <] = ''
The increments here discussed are small finite differences made in ad-
justing practically the conditions of loading. For considerable differences
Equations (A, B, etc.), should be employed.
18 XIT. SARRAU'S FORMULAE FOR INTERIOR BALLISTICS.
The third coefficient varies with r and is equal to for
T i^ Tj. Its value increases with r, but does not exceed ^
except when q is less than -^ which is not likely to happen
in the ordinary conditions of practice.
Comparing equations (21) and (22) it appears that while
in equation (21) the variables are arranged in the order of
their relative importance, in equation (22) the influence of
w on the maximum pressure is less than that of A or r.
Let us consider as a fundamental condition that the maxi^
mum pressure remains at a constant value determined by the
strength of the gun, and suppose but two of the quantities
Wy A and r to vary at a time, the third remaining constant.
First Case, a and r variable, w constant.
The equations reduce to
d t. dt ^
-^ = — and (23)
%'{^y-^ («)
Therefore, if A is varied by changing the size of the
chamber for a given charge, the time of burning must
change correspondingly to the density of loading. In such
a case, if ^>-5%, T increases with A. Hence the conclu-
sion: In order to obtain the greatest velocities we should
use high densities of loading and slow powder.
Second Case. z£^ and r variable ; A constant. (M. L. gun.)
Equation (22) becomes | = , (25)
and equation (21) ^ = f (J - «) ^ , (26)
* That is, that if we increase w by 10 per cent ; then, to fulfill the fun-
damental condition, r must be increased ^, or 7.5 per cent.
XII. — SARRAU'S FORMULi*: FOR INTERIOR BALLISTICS. 19
It follows from equation (18) that since when q is equal
to 0, « = J ; and that when q is greater than 0, n is less than
J, the factor (J — n) is always positive and therefore that the
velocity increases with the charge of powder, and that the
maximum pressure will not be exceeded provided that the
time of its combustion be regulated as required by Equation
(25).
Third Case, w and r variable in a chamber of constant
capacity. We have supposed in the preceding cases that
the volume of the powder chamber can be increased or
decreased at will, and in designing guns to perform certain
work the conclusions reached are useful. Suppose however
that we desire to improve the conditions of loading of an
existing cannon. In this case, since
A =
27.68 w , d t.
wp nivp
dw
(27)
o A
and therefore
dV ,dw dr
(28)
dr dw
r -* w'
(29)
dV ... ^dw
(30)
in which (^— «) is positive.
Therefore, if the chamber is large enough, we may in-
crease the velocity without changing the pressure by using
a larger charge and a slower powder.
Examples.
1. Suppose with a slow powder (;/ = |) we wish to increase
F by 10 per cent, -^ = j^ .= ^ = ^ ^ ... ^«, =
53.3 per cent, and = — 53.3 = 93 per cent. That is, we
20 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS.
would use nearly double the charge of double the size of
grain ; assuming that r is proportional to the size of the grain.
2. Using a quick powder {fi = g) and
~V = To = 32" loo •'• ^"^ =" ^^ P"' "'""'' ^"^ ~r -= ^^
per cent. Or we would use about one-quarter greater charge
of less than one-half greater size.
Fourth Case, w and A variable and r constant.
This corresponds to the use of the same powder in guns
having different chambers.
From the conditions we have
~ = -i~' (31)
y=A'^- (3.)
That is to say; that if we fix the size and shape of the
grain, and wish to increase the velocity, we must increase
both the weight of the charge and the volume of the
chamber.
General Remark,
A review of the preceding cases shows that whenever t
varies, F is a function of n and also of either wov A according
to which one of these is variable.
THE EFFECT UPON PRESSURES AND VELOCITIES OF
VARYING THE TIME OF COMBUSTION.
If in equation (21) we allow only r to vary, we have
_=-;._. (33)
The value of n increases as the modulus decreases; conse-
quently the same relative variation of the time of combustion
has a greater influence upon the velocity as the powder be-
comes slower. See Chapter XI, page 18.
XII. — SARRAU'S FORMUL/K FoR INTERIOR BALLISTICS. 21
(34)
Now, suppose the pressure to vary; under the conditions
equation (22) reduces to
dp^ _ _ ^^ .
Combining this, with equation (33) we obtain the very simple
relation
^=.^%. (35)
V p^
which expresses a relation between velocities and pressures
similar to that between velocities and times of combustion, in
Equation (33).
It has been stated page 12, that the values -^ and ^
may be considered as the limits that the modulus should not
pass. The choice of these limits is justified as follows.
When the modulus is greater than -^ the relative variation
of the velocity depends upon n in equation (35) which under
these circumstances only becomes \ of the relative variation
of the maximum pressure. Consequently, a sensible incre-
ment of the velocity is obtained only with a considerable
increase in the pressure and the energy acquired by the pro-
jectile is imparted at an increased risk to' the gun. This
grows less as the modulus diminishes from -^^ ; because
the value of n increases; but then, from Equation (34), the
relative variation of the velocity corresponding to the same
relative variation of the time of combustion increases, as
shown by Equation (33), so that the influence of accidental
irregularities of the powder upon the velocity continually
grows greater.
It is then advisable to fix an inferior limit for the modulus
so as to preserve uniformity in velocity.
APPLICATIONS.
1. To determine the characteristics a and y5 of a powder.
The most practical method is to use according to circum-
stances either equations (A) or (B) in connection with equa-
S^ Xlt.— SARRAu's FORMULA FOk INTERIOR BALLlStlCS.
tion (D), and to substitute in these equations for V and p^
the mean of several measured velocities and pressures ob-
tained under invariable conditions of loading.
We have then two independent equations involving but
two unknown quantities, a and /?; these may then be deter-
mined without reference to their separate factors.
By the theory, the characteristics are entirely independent
of the gun. In this respect, and also in that they give us
numerically the influence of all the elements of firing, Sarrau's
formulae are more useful than those, like Noble's, described
in Chapter XI.
Having determined accurate values for the characteristics
of a powder, we may compute the velocity and pressure to
be expected in any gun whose dimensions are known, when
the conditions of loading are given; and conversely, the
dimensions may be determined.
Within reasonable limits of variation of the quantities
entering them, the accuracy of the formulae has been abun-
dantly verified.
EXAMPLES.
1. To find the characteristics of Du Font's P. N. (Brown
Prismatic) powder from a single firing of the 8 inch B. Iv.
Steel Rifle. For its dimensions see Table IV.
Data. 2£/=110; fr= 289; A =0.980 ; z/= 1878; /„= 36000;
^/ = 195.75. Equation (D) gives us
«2= i^ — - =0.9706=log-il.98704.
An application of the test mentioned page 6, will show
that the binomial form.ula is applicable; although this might
be assumed for powders of this kind. If then we write
equation (B) so as to combine in each term the quantities
relating to the gun and the conditions of loading, we may
reduce it to the form
XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 23
XF=a-a(3V or jS^"""^^,
a V
in which Fis measured and
— = — > (- /v and Y= — ^^ -.
Substituting in the above the known values of a, X, V
and K we find
log i3 = 1.33725.
Another method is to fire the same powder under very
dissimilar sets of conditions in which W^ w, u, d shall have
different values and to determine the values of V under
these conditions.
We may thus obtain two formulae of the form of the above
value of XV; as these involve but two unknown quantities,
the characteristics sought may be determined.
This method avoids all uncertainty attending the oper-
ation of the pressure gauge; but the former method is gener-
ally preferred as the conditions more nearly resemble those
of practice, and introduce the customary unit of measure-
ment of pressure,
2. To compute the muzzle velocity to be expected from
the 8 inch B. L. Steel Rifle for the preceding powder.
Data. 7i/=105; A =0.935; /^=289.
Computati(
log B =
log^ =
log W\ =
log u^ =
log d-' =
)n of y,
2.30964
1.33725
1.23046
1.14585
1.09691
Computatic
log^ =
log a =
log wt =
log A^ =
log u^ =
log IV-^ =
log d-^ =
log(l-;K) =
log F =
V =
m of V.
2.56635
1.98704
0.75795
1.99276
0.85939
log y
y =
l-y=
1.12011
0.13186
0.86814
1.38477
1.77423
1.93859
3.26108
1824.3
24 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS.
By actual measurement Fwas found to be 1825.
3. To compute the maximum pressure on the breech
under the same conditions as in No. 2. But with a powder
{PO) of which the characteristics are different, viz.: —
a=log-il.97701; y5=log-il.28978.
log^o
=
4.25092
log a*
=
1.95401
log A
=
1.97102
log w^
=
1.51589
log Wi
=
0.61523
log ^-2
:
2.19382
log A
4.50089
A
=
31688
From actual firing under the above conditions the mean
value of A as determined by two independent pressure
gauges was 31700 lbs.
4. In order to avoid injury to valuable cannon, it is custom-
ary at the Proving Ground to make a preliminary trial of
new powders in what is called the proof gun.
Data. w=35.9; «^=181; A =0.8988; ^=8; A=20420.
Find the value of A to be expected when
ze/=90; «^=300; A =0.8018; ^=8.
The first set of data give in Equation (D),
log a2:=0.18085,
hence, we find for the second set of data,
A=41174 lbs.
In actual firing the mean value was found to be 41055 lbs.
Useful Tables.
The following tables give the dimensions of various cannon
of the U. S. land service with the characteristics of different
powders tried in them and the resulting pressures and
velocities both computed and as verified by measurement.
XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 25
They will be useful in solving problems hereafter.
Table IV.
Pow-
der.
Gun.
d
inches.
u
inches.
W
lbs.
w
lbs.
A
V
feet per
sec.
11 ^''
lbs. per
eq. in.
LX...
3'^20B. L. rifle..
3.2
73.2
13
3.50
0.857
1,649
31,000
LXB.
....do
3.2
73.2
13
3.75
0.827
1,756
35,150
IKD..
....do
3.2
73.2
13
3.50
0.857
1,680
29,100
1KB..
....do
3.2
73.2
13
3.50
0.857
1,663
30, £^00
KHC.
12^^ mortar
[2.0
91.6
610
50.0
0.821
932
22,000
MW..
....do
12.0
91.6
610
48.0
788
959
26,250
EVF.
S^^B.L. R Conv..
8.0
98.5
183
45.0
0.792
1,488
32,650
PiV...
8'^B.L. R. S
8.0
195.75
289
110.0
0.980
1,878
36,000
NM..
12'^B.L.R.C.L..
12.0
273.5
800
265.0
0.827
1,688
26,350
NV3..
....do
12.0
273.5
800
265.0
0.827
1,718
26,890
NR...
....do
12.0
273.5
800
265.0
0.827
1,826
32,990
NVi..
....do
12.0
273.5
800
265.0
0.827
1,760
26,625
NVa..
...do
12.0
273.5
800
265.0
0.827
1,756
28,000
IB...
3^M7 M L.R.W.I.
8.175
74.6
10.5
5.469
0.814
1,983
25,000
OB...
12^^ mortar
12.0
91.6
610
52.0
0.854
987
25,250
oc...
....do
12.0
91.6
610
52.0
0.854
942
19,750
26 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS.
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XII. — SARRAU'S FORMULiE FOR INTERIOR BALLISTICS. 27
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OcDi:o-^-3Ciososcno5Cscoi:Di:o?ociTh4i«'«0«oosrfi-^
OOSCOtOCrfM-COOSCOOCOOSOlCO^GOGOOTH-iQTOSOS
00-3COOSOSOtOCOOCOOOOCOtOOCnOO'<l«DtOOl-»-
to M'M-h-lM-hJ^M.M.H'M-M.H*. J^^ ^^^ ^
o'«o"co'^''-3'bT"^7 Oibl or OS CO «0 CD CD OtV CD CD Os''>j^ -;^ ^
f-LOSCOM-C^OOOSlOCOCOGOCDCOQOOOOOajtOOt^OS •
OOOlCOCCOSI-»tOCOCDCOOOOCOtOOh-iOOCOOlM-OH-i
lcotocococoto^oo^tototococototo toto
• or GO O O O CDCO)-^COtOCOOOtOOSCOOO»4^CO
t0t-^O<{OO00O-QC»O0Srf^OC0OOO'<lG0fJ^M-
CAStotococototococotoiocotototococototo toco
OCS 4^ OS Ot -3 cop opp Hi Or H-^ CTf CCJ^sp^jfi-jCi CO tS
O Vj Ot"bT"H-i"--3'*'<}bfl'^ o'h^'m- O^lOCOOStO^CTtOOO
OOiOOOtO— ■JCOOOOOOOlOtOCTCJOlOOO
oooooooooooooooc;toooooo
WfcStOOOOOC^tOCCM'COWOtOl-itOtOOTI-'t-AOOHiW
j Kumber of rounds
considered.
28 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS.
DISCUSSION OF THE COEFFICIENT X^
If in Equation (10), Chapter XI, we replace r^ by we
4
have after reduction, r =. Tc^rr, — rr ji •>
in which u is expressed in feet. But since internal meas-
ures are given in inches we may avoid errors in practice by
writing this
12
in which G = nctAi\ 2 •
2240 g^ n
If in Equations (17) and (D^) we replace the ballistic co-
efficient by C, and collect the constants in both equations
so that
3 (3 ^)W 3 ^ '
these equations will read
_^ ^C wl A^' d^ td N q"" ,^„.
^ =" ^ w^ • ^ ^
^°==-^ Wi did ' (^^)
Substituting these values in Equation (36) we have
X=Za N^ q^--^ (-^y (39)
in which Z = ^-^ = log-^ 0.7394, viz., 5.488.
The factor N, which in Equation (17) was taken as con-
stant, is not absolutely so.* Its value is given in Sarrau as
/(,)=iV," = Z^i^>. (40)
By substituting the value of N impHed in Equation (40) in
q rt
♦ For values of f between yp and -^ ,iV"varies only from 1.012 to 1.056.
XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 29
the factor N* /""' in Equation (89) and calling the result-
ing value Q, we have
This reduces Equation (39) to ^
^ = ^^'e(-|^)*. (42)
Discussion of the Factors of X.
Of the four factors producing %'. Z is a constant ; C
depends solely upon the powder; that is upon its force and
the form of the grain ; Q depends upon the suitability to
the gun and projectile of the kind of powder employed ;
— j depends solely upon the circumstances of the particu-
lar fire considered. Hence, to compare the intrinsic proper-
ties of different powders fired in the same gun, we may
compare their respective values of
The relation between ^ and ^ is shown in figure 2, from
which it appears that while Q is sometimes an increasing and
sometimes a decreasing function of q ; for values of q be^
tween fj^ and -j^, ^decreases slowly from its maximum value
of 1.245, corresponding to ^ = ^q, to a value of 1.159,
corresponding to ^ = -^j*
If the force of all nitrate powders were truly constant,
C = —- = -jj- would depend for its value solely upon the
form of the grain ; and, since within ordinary limits Q does
not vary greatly, we would expect nearly equally good re-
* From this we may conclude that for ordinary approximation the mean
of these values, or ^ = 1.2 may be used. Also that it is not well to
depart much from the inferior limit of g established by Sarrau.
30 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS.
suits from black or brown prismatic powder. But, in the
following illustration, taken from one of the best black pris-
matic powders recently tried, we find /to be so small that C
does not much exceed the value oP 3.0 deduced from
Table I, for ordinary powders of irregular granulation.
We may therefore conclude that the advantage of cocoa
powder consists in its maintaining its force at nearly unity*
without becoming so quick (or slow ; figure 2) as to cause its
value of Q to become unduly small. These considerations
indicate in a general way that its peculiar properties are due
to the nature of the fuel it contains.
Illustrations.
The following data, derived from experimental records,
illustrate the principles discussed :
COMPARISON OF POWDERS.
Gun Sin. B.L.R. 8in.B.L.R.
Powder, kind Bl. prism. Br. prism.
Powder, name O. I. N. Ger. cocoa.
W. 45.0 289.0
Sph. Density 2.9 4.5
V, 1852 1875
A 33075 35900
u 119.8 195.75
a 1.5 1.5
/ 1 ^
* ^ 3
a" 2.45 0.93
(i 0.78 0.21
/. 0.70 0.96
r 0.43 1.59
C 3.16 4.45
q 0.70 0.38
* See Table V, in which the last six powders are cocoa*
Xli. — gARRAU*S FORMUL.fi FOR INTERIOR feALLtSTICS. SI
Q 1.23 1.12
X observed 28.28 34.32
X Equation (40) 28.44 34.87
n 21.26 27.39
Ratio of n 1.00 1.29
If we exchange powders only, we have —
Powder Ger. cocoa. O. I. N.
q 0.19 1.47
Q 0.73 0.50
II 17.95 8.55
Ratio of n 2.10 1.00
That is, that while each powder is best suited to the gun in
which it is actually used, the cocoa powder would be better
for general use, and might profitably be adapted to the siege
rifle by reducing the size of the prism so as to diminish r and
increase Q.
MAXIMUM VALUE OF X,
The value of 11 before deduced, enables us to solve some
very important problems in internal ballistics.
As an example, let us consider the question of how, with
our present knowledge of gunpowder, we may attain the
maximum value of X' Also, let us apply this to a gun the
construction of which limits p^ ; the spherical density of the
projectile being known and the value of ?/ being expressed
8 IV
in terms of the caliber or // rr n d, Let s = — -— be the
spherical density of the projectile.^ The maximum value
of C^ being 4.5, figure 2 shows that the maximum value of
IT, and hence of x^ will require ^ = 0.6.
The maximum value of tj will depend on that of A. The
* See Chapter XVI, page 6.
82 Xn. — SARRAU*S FORMULi^ FOR INTERIOR SAlLISTICS.
specific gravity of some powders is now such that a value of
A =: 1, has been reached. We may consider this a maxi-
mum, as it is rarely exceeded. After deducing general equa-
tions, we will apply them to a typical gun based on the 8-in.
B. L. R. Steel, in which j =z= 4.5 ; ^/ = 24, and take the
maximum value for /„ as 36000 lbs. per square inch, that
being what the records indicate to be a desirable limit.
1. Proper Weight of Charge.
By substituting the values assigned for JV, A, d, t^, q in
Equation (D'), it leads to the following ratio :
^=[log"'n.lll9^']S (44)
In which, by substituting the special typical values assumed
for /(J, n and i", we have w = 0.2 W.
In the 8-in. rifle this would reduce the charge of powder
about one-half.
2. Proper Size of Grain.
If in Equation (16) we place q =s 0.6 and assign values as
above, we have for a general equation, since / = J
r = log " ^2.0799 (^s n)h d. (45)
This shows that, as before stated, the size of the grain
should, in similar guns, vary directly with the caliber. For
the 8-in. rifle, this makes % = 1.0, or, from the preceding table,
the size of the grain should be about 68 fo of its present linear
dimensions; the force of the powder being unity, and the
form remaining unchanged.
3. Maximum velocity.
The maximum value of H = 5.488 X 4.5 X 1.245 = 30.73.
But U = X \ wA = x-:7a 3- = 30.73.
By substituting the value of wl deduced from Equation (44)
XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 33
and reducing, we have*
V= Tlog-^ 2.7355 ^^ ]' ' (46)
Which in the type-gun gives
F= 1716, or ;^=: 46.48.
The largest value of % Y^^ attained with this gun is about
35.0 ; showing an efficiency of about 80 per cent.
Remark.
For sea coast guns, in which the bulk and weight of the
charge is of no special consequence, since the guns are sta-
tionary and magazine room is ample ; the waste of the powder
and the increased volume of the chamber necessitated by the
present use of very large charges may be neglected in favor
of the high muzzle energies required. But as the caliber of
the gun decreases, and its mobility increases, the necessity for
reducing the weight of the charge becomes more important.
This is especially true in the loading of magazine small arms,
the efficiency of which requires the weight of the ammuni-
tion to be reduced to a minimum ; so that the number of cart-
ridges that the soldier may carry will be as great as possible.
* This is independent of the caliber as would be expected from the
principle of similitude, x may also be shown to be independent of the
caliber, by substituting values of W and w in terms of s, and of « in
terms of d.
XIII. — HISTORY OF GUNPOWDER.
CHAPTER XIII.
HISTORY OF GUNPOWDER.
Origin.
Knowledge of the properties of nitre as a supporter of
combustion are attributed to the accidental kindling of the
embers of a camp fire by the salt, often, in India, found effer-
escent upon the surface of the ground. As sulphur is not
essential, its first employment cannot be conjectured. For
its binding properties honey was used at an early date.
Early Use.
The use of gunpowder was at first confined to fireworks
and rockets. These are mentioned in Chinese records over
2000 years old, and seem to be indicated in the account of
Alexander's invasion of India at about the same epoch.
The transition from its use in a paper tube, or bamboo
cane, to cannon of different sizes is indicated by the etymology
of the latter name. The barrel of any fire arm is in French
called canon.
Early Cannon.
The first use of gunpowder as an agent for propelling pro-
jectiles is assigned to the Moors at the siege of Baza in Spain,
about 1325; twenty-one years before the battle of Crecy.
This is about the time that the chemist monk, Berthold
Schwartz, of Freiburg, is said to have discovered its pow-
ers by the accidental ignition of a ternary mixture, lying in
a mortar and covered with a stone.
Owing to the weakness of the early cannon — which were
constructed after the manner of ordinary barrels, sometimes
XIII.— HISTORY OF GTJNPOWDER.
of iron bars welded together longitudinally and hooped with
iron tires, and sometimes even of wood, wrapped with
rope — efforts at first were directed to reducing the strength
of the new agent.
Early Powder.
Therefore, although the best proportions had long been
known, it was often composed of equal parts of the three
ingredients, and sometimes mixed with saw-dust, resin, sand,
or ashes.
It was often mixed and ground by hand as required, and
was used in the form of a fine meal or powder^ from which
its name is derived.
The diminished velocity of inflammation resulting from
the use of meal powder favored the end in view; but, since
the cartridge was yet unknown, the condition of this powder
made it so inconvenient to load the long guns then used
that the efficiency of artillery was much impaired.
Early Breech-loaders.
To overcome this difficulty in loading, cannon at a very
early date were made to load through the breech. But the
arts at that time afforded no means of preventing the escape
of gas through the joint so formed, and such cannon are
comparatively rare.
It will be seen hereafter that the practical utilization of
this principle depended upon the discovery of the self-sealing
gas cheeky the best form of which exists in the metallic
cartridge case, now used for small arms.
But for this essential improvement m^any of the systems
now In vogue are but repetitions of these ancient forms, not
only in principle, but in many details of construction aad
operation.
The reciprocal evolution of the gun and its ammunition
is a striking illustration of the law of continuity.
Xllf. — mSTORV OF rttlKfOWDER.
Men have probably always been equally ingenious in util-
izing the accumulated capital of knowledge at their com-
mand; but the successful application of even simple princi-
ples requires, in many cases, the parallel development of
apparently unrelatec arts.
Intermediate Stage.
It was not until near the close of the 16th century that
cannon, first of copper or its alloys, and then of cast iron,
were made strong enough to resist the pressures due to the
use of the grained powder, the use of which had hitherto
been confined to muskets. This was called corned powder,
vide pepper-corn J barley-cornj coming-mill.
Until about the middle of the present century no great
improvement*: occurred in gunpowder or in cannon. The
reasons for this were the general assumption that gun-
powder was instantaneously converted into gas, and the want
of any apparatus for measuring pressures.
Use of Eprouvette.
Gunpowder was proved by firing it from the Eprouvette, a
small mortar with its axis carefully fixed at an elevation of
45*. The quality of the gunpowder was determined by the
distance to which an accurately fitting ball of a given weight
was thrown by a given weight of powder. Although some
difference existed in the size of the grain used in different
juns, the proof 7'ange increased as the size of the grain dimin-
ished; so that for large guns the size of the grain, as meas-
ured by our present standard, was exceedingly small. See
Chap. XI.
Rodman's improvements.
1. Pressure Gauge.
The late General Rodman, of the United States Ordnance
Department, was the first to investigate the properties of
gunpowder in the modern method.
3tm.— tttStOkV Of 6tlNl>6Wt)£R.
His experiments, conducted with the view of increasing
the effectiveness of the system of cannon which bears his
name, depended primarily upon his employment of the pres-
sure gauge. This was a pyramidal indenting tool, previously
used by him to test the relative hardness of cannon metals,
and applied in the manner indicated for the crusher gauge.
Although open to many grave objections of detail, this
instrument gave useful relative results and served to draw
attention to the very erroneous estimates previously made as
to the pressure exerted by gunpowder. When fired in its
own volume, this had been variously estimated at from 0.7
to 700 tons per square inch.
2. Powder.
a. Mammoth.
Rodman's first step was to recommend the use of large
charges of "mammoth " powder, which was of about three
times the diameter of the largest powder previously used.
This gave satisfactory velocities and moderate pressures;
and, since its manufacture required less granulation than
before, it was cheaper, pound for pound.
b. Perforated.
About 1860, he improved upon this idea by suggesting
the use of perforated powder, made for small cannon in
cylindrical cakes, and for larger cannon in hexagonal
prisms which could be built up into cartridges.
Owing to the great cost and novelty of this powder, and
to the intervention of the civil war, the perforated powder
was used in this country only for experiments ; but the
mammoth powder has until lately been exclusively used for
heavy guns.
DERIVATIVES FROM RODMAN's POWDER.
Russian Powder.
The perforated prisms were experimented with in Russia,
from 1860-1865, being finally made much smaller than
btllt. — kistORY OF GUNPOWDEfe.
Rodman's, and pierced with seven small holes. The powder
was so made in order to adapt it to the muzzle loading guns
then used. See Fig. IB, Chap. IV. This is known as
/Russian prismatic powder.
English Powders.
The English objected to this powder, saying that, owing
to the number of perforations it contained and to its dimin-
ished density, it was liable to break up in the gun.
About 1875, they returned to General Rodman's original
idea, adopting the cubical Pebble powder, the cubes, for
the largest gun , being about lYz inches on the edge.
United States Powders.
In the United States, the mammoth powder was im-
proved upon by the adoption about 1873 of the Du Pont
Hexagonal powder. Fig. 12, Chap. IV.
This and the Sphero-Hexagonal powder, Fig. 12, have
the advantage of great uniformity in the size and shape of
the grains and in the form of the interstices between the
grains. They are also progressive, owing to the diminished
density of the interior of each grain.
This results from the fact that the effect of compression
is not transmitted homogeneously throughout the mass
compressed. The density is always greatest next to the
moving surface.
For reasons given in the text. Flat powders of the Z. X.
type. Fig. 12, are also occasionally used.
Italian Powder.
The Fossano powder, made in Italy, consists of an
agglomeration of dense grains of medium size, set in a
mass of powder meal and pressed to a density less than
that of the individual grains. Its operation is distinctly
progressive.
The principle is applied to other powders, both molded
and of irregular granulation.
Xin. — HISTORY OF GUNroWDER
MODERN POWDERS.
In order to obtain the most effective combination of gun
and powder, each type of gun now requires a special
powder, and some cannon, as mortars, require more than
one powder for each mortar. This increases greatly the
difficulty of supply.
The kind of powder best suited to each type of gun is
still (in 1888) undergoing experimental investigation.
The advantage of adapting the size of the grain to the
size of the gun, upon which for simplicity so much stress
has been laid, is becoming of diminished importance, since
the effects due to increased size may be attained in many
other ways.
Owing to the great number of conditions which require
to be simultaneously satisfied, including the effect of
meteorological conditions prevailing during manufacture,
the powder makers find it difficult to meet the increasing
exactness of the demands made upon them. This applies
even to the duplication of satisfactory samples.
Present Custom.
All large guns of the present day use hexagonal prisms
like the Russian prismatic, but pierced with a single hole.
This is easier to make and its ballistic properties are better.
It is preferably a concrete powder made by consolidating
under pressure small grains of powder previously com-
pressed in the ordinary manner. Mealed powder is some-
times used instead of that which has been grained.
XIV. HIGH EXPLOSIVES.
CHAPTER XIV.
HIGH EXPLOSIVES.
Classification.
Except the chlorate mixtures, the high explosives used in
warfare are all organic nitro-substitution compounds, gener-
ally of the third order, in which 3 atoms of H are replaced
by 3 molecules of NOg.
The most important are Gun-cotton, Nitro-glycerine,
and their derivatives. The derivatives of picric acid are
growing in importance, and so, for special purposes, are the
mono-, di-, and tri-nitro-benzines and naphthalines.
Those which in their operation resemble the mercuric
fulminate are C2i\\t6. fulminating compounds, and include, be-
sides their typical salt, the mixtures in which the chlorates
are used dry.
The demands of civil engineering and the hope of success-
fully adapting these explosives to warfare are constantly in-
creasing the number of those for which both safety and
efficiency are claimed. On the other hand, many, once
famous, are obsolete, so that the following discussion will
relate only to those of which long experience has demon-
strated the essential properties, and to the most distinguished
of recent competitors for the selection of the engineer,
Danger.
Although their composition and violence render the hand-
ling of many as compared with gunpowder, dangerous; yet,
a knowledge of their properties is demanded b- the con-
ditions of the time; and, as with gunpowder and steam, this
knowledge comes principally by experience.
XIV. — HIGH EXPLOSIVES.
The disasters reported with such apparent frequency are
the price of progress toward safety, and point rather to the
enormous consumption of these explosives, often by ignorant
and reckless persons, than to any necessary peril when proper
precautions are observed.
Commercial Importance.
The scale on which these explosives are employed, prob-
ably, as with gunpowder, much greater in time of peace
than in war, appears from the size of blasts fired almost daily
in the Californian mines during the period of their greatest
activity. These blasts often contained 50,000 pounds
apiece.
The great blast at Hell Gate, New York Harbor, in 1885,
contained but six times as much.
The economic value of an explosive depends so much upon
the net cost of the work performed that it is interesting to
note the following relative scale of prices per pound in 1888.
Explosive,
Price.
Proportion.
Gunpowder,
20 eta.
1.0
Dynamite,
50
2.5
Nitro-glycerine,
80
4.0
Gun-cotton,
1.00
5.0
COMMON PROPERTIES OF GUN-COTTON, NITRO-
GLYCERINE, AND THEIR DERIVATIVES.*
Sensitiveness.
When not freed from the acids used in their manufacture,
these explosives are prone to spontaneous decomposition
and tend to form products of a lower order of substitution.
While undergoing decomposition, their sensitiveness is in-
creased, but their efficiency when exploded is diminished.
When properly prepared, they are not sensitive to moderate
* Cadets are advised to review the articles in the Chemistry which
treat of nitro-glycerine and gun-cotton.
XIV. — HIGH EXPLOSIVES.
shock; but friction, the impact of a projectile, or the shock
of discharge may cause their explosion.
Firing.
As a rule, they all explode at about 200°. When ignited
by a flame and unconfined, they burn more or less quietly.
If confined, their explosion is of a low order unless they are
detonated. Their behavior in this respect depends much
upon their mass and the resistance of the envelope. See
Chap. II.
They possess the remarkable property of exploding vio-
lently when gradually heated to about 200°; whereas, if
'dropped upon a red hot iron, they may simply deflagrate.
Detonation,
Owing to the variety of the means by which the mercuric
fulminate may be ignited and to the nature of its product,
it is almost exclusively employed for detonation, preferably
alone and pure, and sometimes with a primer of dry gun-
cotton.
The detonators are commercially known as blasting caps^
exploders^ or fuzes of various degrees of "force " according
to the quantity of fulminate they contain. The fulminate
lies in a thin copper tube, one end of which is closed, and is
ignited either by a quick-match or by the heating of a fine
platinum wire by the electric current. The detonator is
placed in immediate contact with the charge, but should be
so disposed that, if the quick-match is used, the charge shall
not be prematurely ignited.
The mass of the fulminate should bear a certain ratio to
the mass and condition of the explosive; this may neutralize
the advantages on the score of safety which the sluggishness
of the explosive confers.
Long charges may require to have dispersed through them
several detonators in order to maintain the energy of the
explosive wave.
XIV. — HIGH EXPLOSIVES.
Products.
Except Nitro-glycerine all the substitution compounds
yield a large amount of CO, and hence, where potential is
sought, require the addition of an oxydizing agent.
Pressures.
The ordinary gauge being unsuited to measuring the high
pressures of detonation, special devices have been contrived.
General Abbott of the U. S. Engineers, in a series of
experiments (which bear to the high explosives the same
relation as do Noble and Abel's experiments to gunpowder),
suspended in water his gauges at definite distances from
the submerged explosive.
For experiments in air, charges of given weights are
detonated either within or upon similar blocks of lead and
the resulting deformations compared. Or the exact charges
required to burst similar hollow projectiles may be deter-
mined.
Effects.
General Abbott's experiments give the following scale by
which to measure the force^ Chap. II, of explosives. His
results apply only to sub-aqueous mining and indicate the
paradoxical fact that Dynamite is more powerful than
Nitro-glycerine.
He found that the pressures registered by a crusher gauge
varied as the Yi power of the charge and inversely as the
1.4 power of the distance. Or calling / the pressure, %v the
weight of the charge, d the distance, and k a constant vary-
ing for each explosive and for the nadir angle under
water.
3 // kw\*
These comparative results are expressed by the following
table:
XIV.— HtGtt EXPLOSIVES.
Nitro-glycerine, 81 0.93
Gun-cotton, 87 1.00
Dynamite, 100 1.15
• Explosive Gelatine, 117 1.35
a result quite different from that of Chap. II.
On the other hand, extended practice in mining operations
under ground confirms the relative useful values of the high
explosives as determined by their potentials and stated in
Chap. II.
Three spheres surround the center of the explosion:
1. The sphere of pulverization.
2. The sphere of rupture or dislocation.
3. The sphere of fracture or fissure.
The relative dimensions of these spheres vary with the
force and potential of the explosive.
Tamping.
The great rapidity of the reaction renders special tamping
unnecessary, since the pressure of the atmosphere suffices to
produce many of the effects desired. This is the origin of
the common idea that such explosives act downward. This
property is particularly valuable in military operations where
time is precious.
The best results, however, are found when they are
tamped. Even a thin layer of earth or water greatly in-
creases their effect. For a similar reason the mass of the
charge is best placed between the detonator and the object
to be destroyed.
Example.
Long iron tubes filled with dynamite have been detonated
in air without converting all of their contents. When the
tubes were submerged, the entire charge was detonated,
Chap. II, page 5. The accidental explosion of charges which
have been imperfectly detonated leads frequently to disaster,
and so, it may be said, does tamping with an iron bar.
XIV.— tttGli eX!>L6S1VES.
Physical Condition.
The greater the density of the explosive the smaller the
bore hole required to receive it, and hence the greater its
economy.
Plastic explosives are valuable since they may be used in
irregular cavities, and in those opening downward; they may
also be rammed after loading so as to increase the value of A .
The advantages in this respect of the liquid state of nitro-
glycerine made it very popular at first; but its tendency to
leak in transportation and to filter through crevices in the
rock is very objectionable, since in a thin film it is easily
exploded by impact and especially so by friction. Cans
containing it have been exploded by twisting the cork. The
granular form is advantageous on account of the ease with
which it may be loaded into bottle shaped cavities, as in
hollow projectiles and torpedoes. Rigid prisms form con-
venient packages for transportation, but require cavities
of a special form to develop the best results.
Cold.
When in a liquid or plastic form, the high explosives have
their sensitiveness much impaired by freezing. This occurs
at a little above 0°.
The force and sensitiveness of loose dynamite are not im-
paired by its freezing.
Heat.
In such cases thawing is dangerous unless very gradually
performed, as by the heat of the body, of manure, or of luke-
warm water.
The nitro-glycerine in frozen dynamite of the solid form
tends to exude on thawing.
The sensitiveness of an explosive increases with its
temperature.
Water.
Nitro-glycerine and gun-cotton are insoluble. Water tends
to displace the nitro-glycerine from dynamite' which has been
XTV. — HIGH EXPLOSIVES.
compressed; but, strangely, has no such effect upon that
which is loosely granular. For this reason sub-aqueous
torpedoes are charged with loose dynamite.
Owing to its greater density the displaced nitro-glycerine
settles to the bottom of the vessel containing the dynamite,
whence it may exude and lead to the consequences noted
above.
When dynamite or gun-cotton is wet, it ignites with great
difficulty but may be detonated by a powerful primer. Any
soluble addition is of course removed by water.
TTse.
Except gun-cotton and the picrates, all the high explosives
have so far been employed only for mining and demolition,
and to a limited extent in pyrotechny.
Efforts are constantly making to adapt them to the burst-
ing charges of hollow projectiles, by affecting either their
condition, the construction of the projectile, or the source
of energy by which it is thrown.
Such attempts have not yet (1888) wholly passed beyond
the stage of experiment and, though occasionally successful,
have yet to endure the test of long continued firing. In
many cases it appears that failure comes less from explosion
under the initial shock than from the friction due to the
rotation of the projectile. If the initial shock or acceleration
be diminished, flatness of trajectory is sacrificed or the gun
is made inconveniently long; if the rotation of the projectile
is abandoned, inaccuracy results.
The sensitiveness of the explosive tends to cause a prema-
ture explosion on impact against armor and its force tends
to pulverize the envelope into ineffective fragments.
The sphere of such explosives appears to be confined to
the ordinary sub-aqueous mines or to their employment in
aerial torpedoes, exploding under water in the vicinity of a
vessel, as in the Zalinski system; or against earth works as
XIV. — HIGH EXPLOSIVES.
in the new gun-cotton shell now employed in Germany.
This projectile has been fired with charges as great as
110 lbs. Captain Zalinski has fired a mixed charge of high
explosives weighing 500 pounds to a distance of one mile.
Some of the high explosives, notably the gun-cotton class,
have been used for fire arms, principally in fowling pieces,
for which the reasons assigned, Chap. XI, page 18, particu-
larly adapt them. The absence of smoke is a considerable
advantage. They have even been employed by the Austrians
for field pieces.
The uncertainty as to the order of the explosion resulting
from accidental variations in the value of A , has caused their
use in cannon to be abandoned. For the former purpose it
is still unfortunately common.
GUN COTTON.
Forms.
This occurs in three forms; viz.:
1. In the flocculent or pulverulent form, made from cotton
wool as indicated in the chemistry.
2. Prepared from the first form by pulping and com-
pression to a density a little greater than that of water.
3. In grains, made by disintegrating the second form
above.
Condition.
The first form is always used dry and is employed only in
pyrotechny. The other two are used either wet or dry, and
when wet, are sometimes protected by a water-proof coating
to retard evaporation.
Firing.
Dry gun-cotton ignites at a lower temperature than any
other of the common explosives. Its combustion may be
retarded by compression and the addition of a gum.
When it contains from 20 to 30 per cent of water, it can-
XIV.— HIGH EXPLOSIVES.
not be ignited until the water has been evaporated by the
flame. One ton of loose wet gun-cotton has been burned
with safety in a bon-fire
Detonation.
When wet and compressed, it may be detonated by using
a sufficiently large primer of dry gun-cotton. Its incorpo-
ration in a dry state with paraffine is said to yield the same
results as to safety as when it is wet, without diminishing
its sensitiveness to detonation. This avoids the difficulty
of preventing evaporation.
Reaction.
This varies with the value of A and with other conditions,
but may be represented by the following formula,
2QH7(N02)3 05=70H2H-3C02 + 9CO + 6N.
To increase its potential a nitrate or chlorate is often
added, the latter being the more energetic.
Gun-cotton mixed with one third its weight of a nitrate
forms Tonite, an explosive much used in the Californian
mines.
Advantages.
Compared with gunpowder, its manufacture is less danger-
ous and the apparatus can easily be improvised from the
paper-mills.
Since it forms no dust and can be kept wet, it is safe in
transportation and in store.
In mining, as in fire arms, it yields no solid products, and
in sub-marine mining it can be used under water; having
even been detonated in a net.
Disadvantages.
Besides those which relate to its sensitiveness and vio-
lence, the principal objection to its employment in artillery
applies to the absence of smoke which serves to mark the
bursting point of a distant shell.
10 XIV. — HIGH EXPLOSIVES.
MANUFACTURE OF GUN-COTTON,
rormer Method.
Gun-cotton, like nitro-glycerine, was discovered about
1846. It was first made by dipping cotton wool into mixed
sulphuric and nitric acid and washing thoroughly the gun-
cotton wool so formed. But it was found to be impossible
to remove the free acids from the tortuous capillary tubes
of which cotton wool is composed, and the resulting product
was dangerous in store.
Abel's Method.
The tim? of manufacture has been much reduced and the
quality of the product improved by the following method.
Instead of using raw cotton, often containing impurities
which are liable to cause spontaneous decomposition, cotton
waste is employed. This has been previously spun mto
yarn for cloth and is therefore mechanically clean.
Preliminary Operations.
Its conversion into gun-cotton follows the method previ-
ously taught, the essential points being: —
1. To prevent the continued action of dilute acids and
the consequent formation of di-nitro-cellulose (Collodion
cotton), by removing the cotton after its first immersion
to a fresh mixture of acids in which it is soaked for several
hours. After each immersion the excess of acid is removed
by wringing.
3. To prevent an undue rise in temperature, by making
the first immersion in small quantities at a time, and sur-
rounding the vessels containing the cotton with running
water.
3. To prevent the access of water to these contents. A
drop of sweat may cause the acid cotton to ignite.
Final Operations.
After the final wringing, it is washed by plunging small
quantities of the cotton into large quantities of water.
XIV. -HIGH EXPLOSIVES. 11
The cotton is then reduced to a pulp by the rotary knives
of the rag engine used in paper making. These operate
under water.
Being now in short tubes, the washing can be thoroughly
performed by means of the paper maker's poacher. This is
a vertical water wheel working on one side of an oblong
trough through which a longitudinal partition extends
nearly from end to end.
After a protracted washing in the poacher, the free acids
still remaining are neutralized by some alkali; this having
been washed out, the pulp is, after draining, ready for the
hydraulic press.
After pressing the cylinders they are carefully and slowly
dried; or, they may be kept wet as previously stated.
A similar product has been made from bran or straw, and
is known djs, fulmi-bran^ etc.
NITRO-GLYCERINE.
Manufacture.
The preparation of this explosive has been sufficiently
described in the course of chemistry The principal points
to be observed are: — m
1. To prevent a rise in temperature by pouring the
glycerine slowly into the mixed acids, and to preserve a low
temperature by a jacket of running water and by agitating
the mixture by a current of air.
2. To wash the product thoroughly with cold water and
finally with an alkaline solution. The addition of cold water
precipitates that portion of the nitro-glycerine which remains
suspended in the heavy acid liquid.
Too much importance cannot be attached to the entire removal
of free acid. The detection of free acid constitutes one of
the most important tests of this product.
12 XIV. — HIGH EXPLOSIVES.
When first made, it is white and opaque; \t soon assumes
an oily appearance which, if well made, it retains. Its density
is about 1.6.
Reaction.
The explosion of nitro-glycerine gives the following
reaction,
2C3H5(NO,)3 03=6CO,+ 6N4-0 + 5 0H«.
Following a general law, since its composition furnishes
an excess of oxygen, the reaction is sensibly constant and is
found to agree with that deduced on theoretical grounds.
In this respect it differs from most of the explosives.
Special Properties.
As ordinarily used, this is the most powerful of the ex-
plosives, excelling both in potential and force.
It was originally thought to be perfectly safe when frozen;
but it has since been found that, when in this condition, it
can be exploded by a powerful shock if concentrated upon
a mass sufficiently small.
DERIVATIVES OF NITRO-GLYCERINE.
Owing to the dangerous properties of liquid nitro-
glycerine, it is no longer employed except with an absorbent
dase or dope which will prevent its exudation.
The absorbents are of two kinds: —
I. Those which are chemically inactive, such as kiesel-
guhr (also known as " tripoli " and " electro-silicon "), mica-
ceous scales, and, for its alkaline properties, magnesium
carbonate.
II. Those which are chemically active.
These derivatives have a density of about 1.6. They are
usually plastic, which gives them great practical utility.
XIV. — HIGH EXPLOSIVES. 13
I. MECHANICAL ABSORBENTS.
Dynamites. Giant Powder.
Of these absorbents the best is kieselgiihr. This consists
of microscopic shells, the cavities in which retain the liquid
and protect it from ordinary shock. Kieselgiihr has remark-
able properties as an absorbent; it can take up three times
its weight of nitro-glycerine without exudation, even when
under considerable pressure.
Different grades of dynamite are made depending upon
the proportion of nitro-glycerine which they contain. The
highest is called No. 1.
Owing to the knowledge of the properties of this explosive,
gained by the torpedo service and by private industry, it
may be called the standard high explosive of the United
States. For torpedoes its merits consist in: —
1. Its force.
2. Its permanency under the varied conditions and
accidents of service.
3. Its safety and convenience in loading.
4. The readiness with which it may be procured in the
market.
This was true in 1881. Since then several explosives have
been invented which threaten its supremacy,
Preservation.
Although used for special purposes in the granular form,
in which it resembles brown sugar, it is generally put up
compressed in cylinders wrapped tightly with paraffined
paper. These are packed in sawdust in wooden boxes,
preferably made light, without metallic parts and coated in-
side with a water-proof varnish.
When received, the boxes should be partly opened to
facilitate the discovery of the nitrous fumes that accompany
the process of spontaneous decomposition. Their contents
14 XIV. — HIGH EXPLOSIVES.
should be tested for exudation and acidity, and should be
carefully kept from water,
• II. CHEMICAL ABSORBENTS.
Properties.
Absorbents of this class reduce the quantity of nitro-
glycerine required to produce a given effect and so cheapen
the product.
Their judicious selection adds greatly to the energy
developed by the nitro-glycerine alone, so that the economic
value of the explosive may increase more rapidly than does
'its percentage of nitro-glycerine.
For sub-aqueous explosions it appears that with any par-
ticular base there is an economic gain in increasing the per-
centage of nitro-glycerine up to a certain point, but that
beyond that point the advantage ceases. There appears to
be a decided advantage in gelatinizing the nitro-glycerine
before its absorption.
See Forcite and Explosive Gelatine, /<?j/.
Classification.
The chemical absorbents may be conveniently divided
into two general groups, according as they are simply com-
bustible, or in themselves high explosives.
Class I. A combustible dope.
When finely ground cellulose is treated with super-heated
steam, it is converted into a jelly capable of absorbing 19
times its weight of nitro-glycerine. With or without the
addition of nitre, it forms Foi^cite^ a most powerful explosive.
Gunpowder, preferably made after Col. Wiener's method,
Chap. IV, may be coated with nitro-glycerine, the detonation
of which detonates powder, Chap. XI, This foruas the
Jtidson powder.
Class II, A high explosive as a dope.
The most famous is known as Explosive Gelatine. This
consists of about 93 per cent of nitro-glycerine with 7 per
cent of collodion gun-cotton (di-nitro-cellulose). The
addition of 3 or 4 per cent of camphor greatly diminishes
its sensitiveness and adapts it particularly for warfare.
It is generally a transparent jelly, but often becomes hard
and opaque. The fulmi-bran, page 11, may replace the
collodion cotton.
Although found by General Abbott to be stronger than
nitro-glycerine, it is much safer, particularly against shock.
It has been found to burn freely without explosion, even
when confined, and to resist perfectly the action of water.
It requires an initial primer for its detonation and the
weight of the primer required increases as its sensitiveness
diminishes.
When the collodion cotton is not thoroughly purified, this
explosive tends to decompose spontaneously. Otherwise it
is quite stable.
New smokeless powder.
By reversing the proportions of nitro-glycerine, and col-
lodion used in explosive gelatine, and retaining the camphor,
the compound becomes plastic when heated. It may then
be pressed into sheets or drawn into wires or rods which, on
cooling, become horn-like, like the celluloid of commerce.
The reduction of w and the increase of \i are reported to
give in the 6 in. Rifle a value oi %•=. 100 -f-. Its tactical
advantages adapt it particularly to rapid firing arms of small
caliber. The special difficulties to be overcome refer to the
volatiUty of the camphor and to the erosion of the bore re-
sulting from the heat of the explosion. See Chap. IX, Notes.
NITRO-BENZINE OR -BENZOLE.
The preparation of this resembles that of nitro-glycerine,
16 XIV. HIGH EXPLOSIVES.
the mono- (liquid), and di-, and tri-nitro benzines, (crystal-
line) being formed. (Bloxam, Art. 325.)
These substitution products are in themselves inexplosive,
and show by their composition, C^ H^(N02)g_j, ^^^ necessity
for the addition of an oxydizing agent.
Rack-a-Rock is made at the time of its employment by
saturating K CIO3 with crude mono-nitro-benzine, or even
with the "dead oil" from the gas works which has been
diluted with CSg containing a small proportion of sulphur.
By exposure to the air the CSg evaporates, leaving the finely
divided sulphur on the salt but protected by the lubricating
property of the oil or nitro-benzine against explosion by
friction.
When the dope is finely ground and the charge exploded
by a powerful primer it is found to be nearly as powerful
as dynamite No. 1.
This is the only chlorate mixture which has been found
safe in practice.
Helhofite^ as used in Germany for armor piercing pro-
jectiles, is another of the Sprengel Safety Mixtures pre-
pared as wanted by dissolving di-nitro-benzine in nitric acid.
Bellite (La.tin: Bel/um — War), is a recent Swedish explosive
made of about -J tri-nitro-benzine and | ammpnium nitrate,
incorporated together.
This is distinguished by its great safety under all con-
ditions and by its greater potential as compared with
dynamite,
Only dampness affects it. It is almost incombustible,
smouldering only by the continued application of flame.
It is so insensitive to shock that the detonation of itself upon
a box filled with the explosive, or the explosion of gunpowder
in its midst fails to explode it. A wad of it has been fired
from a fowling piece against a target without injury to either.
It gives no injurious gases, nor flame, which properties.
XIV. — HIGH EXPLOSIVES. . 17
together with its high potential, particularly adapt it for the
coal miner. It is also cheap and indifferent to variations in
temperature.
Tamping is necessary to develop its full effect, even when
detonated ; but when tamped and detonated, it is about 33
per cent stronger than dynamite.
The crystaline form of the two ingredients of Bellite
would appear to insure its stability in store and to make of
it one of the best high explosives where potential is required,
as in torpedo shells. For sub-aqueous mining, dynamite is
probably better suited.
PICRIC ACID (TRI-NITRO-PHENOL).
This is made by the action of nitric acid on carbolic acid
(phenol). It occurs in slightly soluble plates of a bright
yellow and is much used in dyeing. Unconfined, it will not
explode by heat, but may be detonated.
When mixed with gun cotton dissolved in ether, it is said
to form the new French explosive, Melinite.
Emmensite is a recent American explosive, prepared from
crystallized Emmens acid and a nitrate. The acid results
from the solution of picric in nitric acid.
The claims made for this explosive resemble those noted
under the description of Bellite. It is (1891) under trial in
the United States.
THE PICRATES.
The potassium and ammonium salts are the only ones
employed.
The former with the addition of nitre and charcoal forms
Designolle's powder. This was found too dangerous for
use, as it tends to detonate on ignition.
The ammonium salt is less sensitive to shock and burns
in the air like resin. With the addition of a nearly equal
18 XIV. HIGH EXPLOSIVES.
part of nitre and prepared like ordinary gunpowder, it forms
the powder of Briigere. In small arms, a charge less than
one half the charge of ordinary gunpowder suffices to pro-
duce the same effects. This is of importance since it enables
the size and weight of the cartridge used in magazine rifles
to be greatly reduced.
The powder yields no smoke or fouhng but is hygroscopic.
It is believed that the new powder used in the French
Lebel rifle is a variety of Brugere powder.
THE FULMINATES.
The mercuric salt is the only one of practical value. Its
efficiency depends rather upon its force and the nature of
its product than upon the heat evolved by its decomposition.
This follows from the reaction,
C2HgN2 0a=:2CO + Hg + 2N.
Its force is said to be nearly 10 times that of gunpowder.
When dry it is easily detonated by shock, friction, a tem-
perature of about 200°, or by the strong acids.
Certhelot finds that even so stable a gas as nitric oxide
is dissociated by the detonation of mercuric fulminate.
While for detonation it is preferably used pure, for igniting
the charges of fire arms it is mixed with an oxydizing agent
and often a combustible, in order to increase the length of
the flame. Powdered glass 's also added v/hen the salt is
expiod'^d by percussion.
Its safety in manufacture depends upon its absolute in-
explosiveness when wet. If placed upon a metallic surface,
it tends to decompose; hence, percussion caps are varnished
before they are primed.
Under no circumstances should the fulminate be carried or
stored near any of the high explosives.
XIV. HIGH EXPLOSIVES. 19
CHLORATE MIXTURES.
Since their discovery, a century ago, frequent efforts have
been made to utilize the chlorate mixtures in mining and as
a substitute for gunpowder. Their extreme sensitiveness
to friction has almost uniformly caused their employment
for such purposes to result in disaster.
Mixed with Sbg S3, the potassium chlorate forms the friction
composition used in cannon primers. It is also employed in
pyrotechny to compensate for the cooling effect of sub-
stances employed to give color and brilliancy to the flame.
GENERAL REMARKS ON THE EMPLOYMENT OF
THE HIGH EXPLOSIVES.
In Guns.
Their employment has always failed, except for small arms
and as noted page 8.
For Bursting Charges of Hollow Projectiles.*
Explosive gelatine has been occasionally fired without
premature explosion, by the use of diaphragms within the
shell. See also gun-cotton, and the experiments with the
Zalinslii gun before noted.
For Demolition of "Walls, etc.
Unless the wall is very strong, the best results in breach-
ing appear to follow the detonation of the explosive at the
base of the wall and at a few inches distant. This distrib-
utes the effect, and racks and fissures the wall so as to facili-
tate its destruction by hand.
Exploded in immediate contact, a smaller hole is said to
be made and the energy to be expended in giving motion
* The premature explosion of such bursting charges by the shock of
discharge is often attributed to the sensitiveness of the fulminate neces-
sarily used in the detonating fuze.
20 XIV. — HIGH EXPLOSIVES.
to but few fragments. About 10 lbs. of dynamite will open
a practicable breach in a two foot stone wall. Tamping
would reduce the size of the charge required.
Houses, Palisades, etc.
About 5 lbs. of dynamite will wreck a small stone dwelling
if exploded near its center, since it tends to overthrow all
the walls instead of blowing out through the nearest one.
The same quantity suffices for a linear yard of ordinary
palisading. A pound of dynamite will shatter a 12 inch
bridge timber.*
Disabling Cannon.
When time permits, bring the gun as nearly vertical as
possible; fill it with water, plug it, and explode simultane-
ously two one pound charges of gun-cotton, one at the
bottom of the bore and one in the chase. When time is
scant, insert a shot within the bore, and place on top of the
chase, between the shot and the muzzle, two pounds of gun-
cotton, laying over it a filled sand bag or a sod. Such charges
are said in the English Manual to suffice for the lighter
natures of sea coast guns.
It is found to be more advantageous to attack the cannon
themselves, than to waste time and explosive material on
their carriao:es.
♦These directions are intended to apply only to hasty operations.
When time permits, the best results will follow from placing the charge
under or within the structure to be demolishedo The quantities are
approximate.
XV. — M£T ALLURG Y.
CHAPTER XV.
METALLURGY.
I. TESTING MACHINES.
Necessity.
The physical properties of a metal may sometimes be in-
ferred from a knowledge of its chemical composition, but so
many other causes may contribute to modify these properties
that chemical analysis should be depended on, rather to indi-
cate the existence of certain limiting or possible conditions
than to declare the extent to which these conditions have
been approached. Thus, what a metal is becomes subordi-
nate to what it can do ; and its proof is more conclusive than
even its chemical inspection.
Requisites.
A complete testing machine should include means for de-
termining the varying strains under tensile, crushing, trans-
verse, torsional, and shearing stresses. But for simplicity,
and on account of the comparative ease with which all stresses
can be referred to that first named, such machines are gen-
erally of the tensile type.
Comparisons.
For establishing comparisons the stresses are usually meas-
ured per unit of minimum area of cross section, and the
strains per unit of length between established points on the
specimen. But if the form and dimensions of the specimens
are constant, absolute measures may be compared. In the
following discussion stresses and strains will, unless otherwise
stated, be taken per unit of section and of length.
XV. — metallurCV.
In the United States stresses are given in pounds per square
inch; in England in tons of 2240 lbs. per square inch; in
France in kilogrammes per square centimetre; in Russia and
Germany in atmospheres.
Form of Specimen.
Since the deductions from proof are conclusive only as to
the actual piece tested and are inferential as to all others,
the above precautions for the comparison of properties are
not wholly sufficient. The general • rule in experimental
comparisons, of dealing with but one variable at a time,
should be followed by subjecting specimens as nearly as
possible in size and shape lik>e those to be actually employed
to the same kind of stress that they will be called on to sustain.
But the capacity of the machine rarely permits this, and,
as its strength limits the maximum cross section, the length
of the specimen in units of the corresponding diameter should
be approximately proportional to that of the finished piece.
The size of the machine and the cost of preparing specimens
limit this; so that the length of the specimen is generally
about 4, 6, or 8 diameters, with a tendency to increase.
The specimen is held so that its axis coincides with the
action line of the force; otherwise, it will rupture in detail,
or tear across. This condition is fulfilled by making the
specimens truly cylindrical with enlarged concentric heads,
figure 3, by which they may be held in the machine.
Form of Record.
This states the strains due to certain stresses. They are
functions of each other, and the relation may be expressed
e —f{w),
in which e represents the strain, or the change of form pro-
duced by applying the stress w. The stress is taken as the
independent variable since it can be more readily controlled
XV. — METALLURGY.
than the strain. Inasmuch as conditions vary too much, and
are not yet sufficiently understood to enable the law of this
function to be analytically expressed, that which governs any
particular case may be best determined empirically:
1st. By forming successive orders of difference in the
observed value of the function for equal increments of the
variable w.
2d. By plotting a line constructed from these co-ordinate
values. Such a line is called a strain diagram.
3d. By constructing a strain diagram automatically during
the progress of the test.
The order of preference is as follows:
The first method when great accuracy is required and
when a micrometer can be used.
The second and third when general comparisons are to be
made.
The second to the third when the expense of the registering
apparatus is objectionable.
In general, rectilinear strains can be measured more accu-
rately than they can be registered by any mechanical apparatus.
ELASTICITY.
Elastic Limits
In operating the machine the stress is very slowly and stead-
ily applied, either directly by hydraulic pressure, or indirectly
by a screw acting in combination with levers. The stress is
relieved at intervals and the specimen permitted to recoil.
The difference between the strain e and the recoil r is the
set s, ov e = r -\- s. The set may diminish in time and be-
come the permanent set, but the first temporary set is that
generally recorded. Sets probably occur under all stresses,
but may be too small for measu^-ement. This may be illus-
trated by the curves, figure 1, which are very much exagger-
ated.
Let 00\ 00" represent certain stresses resulting in strains
O'p' , 0"p'\ etc. Each of these strains is by definition com-
XV. — METALLURGY.
posed of the recoil r — r'p' and the set s = O'r' , etc.
Starting from 0, as the stresses increase the recoils and sets
both increase, but the sets less rapidly than the recoils.
After a certain stress, Z, the line of sets becomes nearly
parallel* to that of strains, so that for a given increment of
stress the increments of strain and set are nearly equal. The
stress corresponding to L is the superior limit of the stresses
for which the sets increase less rapidly than the recoils, and
the inferior limit of those for which the sets increase more
rapidly than the recoils. This stress is called the Elastic
Limit.
Since below the elastic limit the sets are relatively small,
and above it the sets are relatively large, when compared
with the recoils, it may be defined as the limit of the stresses
within which sets may be neglected and beyond which recoils may
he neglected ; or the limit separating the consideration of the
elasticity of the metal from that of its ductility.
It may be determined —
I. By finding the stress corresponding to the first significant
term of the second order of difi"erences of strains or sets.
II. By inspection of a diagram such as represented in fig-
ure 13.
Coefficient of Elasticity.
If the strains below the elastic limit be considered directly
proportional to the stresses, this portion of the line will be
straight, and the tangent of the angle included between it and
the axis of E will be proportional to the reciprocal of the
rate at which the specimen submits to (i.e., directly to the
rate at which it resists) the stress. This is called the coeffi-
cient of elasticity, or
^ _ r^ _ ^ ^ /Wheeler, \
^ ~ Z ^ 7 ' V Eq. 1. y
* As a rule, the recoils increase gradually throughout.
XV.— -METALLURGY.
Elastic Work, etc.
The area bounded by the diagram, the axis of E, and a
line drawn through any point of this axis parallel to the axis
of PFis evidently proportional to the work done by the corre-
sponding stress.
For a given stress O O'", the area, O e r"', is proportional
to the work of permanent deformation corresponding to the
stress O O'". Similarly the difference between the areas
0^'/'"and O^r'" is proportional to the work of restitution,
or the elastic work, following the same stress. The term
Elastic Work, as a measure of this elastic property, also
known as toughness, is properly applied only to the area
under the diagram at the elastic limit.
The total area under the diagram up to the point of rup-
ture is proportional to the potential work of deformation. While
for mechanical units, such as posts, beams, levers, chains, this
property is valuable; in the more complex structures required
by the principle of the independence of function, such as
wheels, trusses, and built-up guns, the elastic work, which
comprises in its measure both the elastic limit and the coeffi-
cient of elasticity, is much more important.
In such structures the permanent change of form of one of
the units may derange the rest; and generally the elastic
work may be counted on repeatedly, while the work of per-
manent deformation can be utilized but once.
FORMS OF TESTING MACHINES.
Tensile.
This is the form most generally used and upon the indica-
tions of which modern gun construction is based.
The sketch, figure 2, shows a simple apparatus extempo-
rized for testing the sheet metal from which small-arm car-
tridges are made. The strains were taken from the punch-
maVks a,b, and plotted.
For testing the metal of which cannon are made, a form of
XV — METALLURGY.
tensile machine recently devised in England consists of a
hard steel cone, which by a blow from a falling weight is
driven through a ring cut concentrically from one of the
short cylinders composing the gun.
Transverse.
The simplest of all is for transverse stress. The specimen
is placed on rollers kept at a constant distance apart. One
objection to transverse machines is the difficulty of separating
the tensile from compressive strain.
A valuable modification of this form of machine is that
which tests the capacity of the metal to endure extreme bend-
ing, even to the extent of working its ends back and forth as
long as the tenacity of the specimen permits. The bending
angle thus determined is one of the readiest and best tests for
ductile material.
Torsional.
Although a torsional strain is even more complex than the
transverse, yet, owing to the ease with which the power
of the lever may be increased; to the simplicity, compact-
ness, cheapness and rapidity of operation of machines of this
class; and to the ease with which the relative rotary motion of
the parts may be made to record the circumstances of the
test, this method is very valuable where great accuracy is not
required, nor variation in the form of the specimens expected.
For the machine used in this department of instruction, the
specimens are of the standard size shown in figure 3. This
requires direct comparison of results.
Thurston's autographic torsional testing machine, fig-
ures 4, 5^ G, 1, 8.
Description.
Two similar wrenches with rectangular jaws, facing each
other, are carried by the A shaped frames shown in figure 4,
and revolve independently about axes which are in the same
XV. — METALLURGY.
Straight line. The wrenches are not connected except by the
interposition of the specimen, which is supported axially by
the conical points shown, and kept by folding wedges from
revolving in the jaws. The' arm B of one wrench carries a
weight W at its lower end. The other wrench is revolved by
a worm gear, P.
To the frame A is secured a guide curve G, of such form
that its ordinates are proportional to the successive torsional
moments exerted by B during its revolution.
The pencil-holder/^ is carried on the arm B, to which it
is pivoted at a and b so as to oscillate in a plane perpendicu-
lar to that in which B rotates. A spring, sp^ keeps the pen-
cil-holder in contact with the guide curve.
Operation.
As the worm gear revolves it tends to revolved and to raise
PTby means of the specimen -S".
As B revolves, the roller r rides on the edge of G so that
the pencil is displaced laterally in a plane perpendicular to
that of its rotation; the object being to establish as follows a
system of rectangular co-ordinate axes of stresses and strains,
to which the position of the pencil may be referred:
I. To make the lateral displacement of the pencil propor-
tional to the stress, W. Since PTis proportional to the mo-
ment of ^, which, since the weight of B is constant, is pro-
portional to the sine of the vertical angle 0, figure 7, the
edge of G is so formed that when B is rotated, the pencil
will trace upon the cylinder D a curve the equation of which
when developed on a plane surface is _y = ^ sin 0. In
this equation J/ is the variable ordinate of the curve measured
along that rectilinear element of D upon which the pencil
rests when the inclination of ^ = 0, and <2 is a coefficient
depending upon the maximum value of _y permitted by the
construction of the machine.
II. To make the peripheral displacement of the pencil
XV. — METALLURGY.
proportional to the strain, E. Calling ;t: the developed path of
the pencil along a circular element of the cylinder, we have
X '. (p>^ \\%TCr \ 360°, or0 =-— jvand .'.y=^ as'ml- .x\
^ ^ %7tr -^ \Z7tr j
The circumference of the drum is 36 inches and its length
is 5 inches; therefore, taking x in inches.
jj^ = 5 sin (10 . x).
Such a curve having been constructed upon paper may be
wrapped around D, and the edge of G be adjusted so as to
make the point of the pencil follow the curve as B is revolved,
D being at rest.
The strain is evidently proportional to the rotation of D
relatively to that of the pencil ; while the stress is proportional
to the angular displacement of the pencil. This will be un-
derstood by imagining lines traced by specimens which are
either perfectly extensible or perfectly inextensible. Such
lines are limits for all natural specimens which will cause in-
termediate lines to be traced that will express the relation
e ^/{w).
Form of Record.
The record is made on a piece of cross-section paper ruled
in inches and tenths w^rapped tightly around the cylindrical
drum D.
The weight W is so taken that the maximum moment
= 500 lbs. ; therefore, since the ruling is 5 inches wide, one
division of the paper measured across its width represents a
moment of 10 lbs., and, since 2 tt r = 36 inches, one division
along the length of the paper = 1° of strain.
In raising the arm by the specimen, the moment of W is
in equilibrio with the torsional stress plus the frictional mo-
ment of the journal /; this last is constant and is allowed
for in standardizing the machine.
XV. — M£tALLURGY.
INTERPRETATION- OF THE RECORD.
For torsional test this is facilitated by considerinij the spe-
cimen as consisting of parallel fibres, at first rectilinear, and
elongating under stress in a helical form. The general form
of strain diagrams, whether made by torsional or tensile test,
is so similar, that although the following discussion partic-
ularly refers to the results of the torsional test, its application
may be considered as general.*
General Case.
The combined effect of stress and strain is seen in the
typical diagrams, figure 9.
In curve / the elastic limit is plainly shown at a. The
convexity of the first portion is probably due to the prelimi-
nary strain of the exterior fibres occurring in soft materials.
The line then becomes sensibly straight, its inclination
determining the coefficient of elasticity, -— , or the rigidity
of the specimen. Beyond the elastic limit it becomes wavy,
indicating deficient homogeneity as to structure ; the fibres
are then supposed to slip. Having adjusted themselves they
* The following relation between torsional and tensile stress has been
approximately determined by experiment. Let T = tensile stress in
lbs. per square inch; Ti = torsional stress in lbs. ; 9 = angle of torsion
in degrees. Then, for steel and probably for other ductile metals,
T= 7\ (300 -^\.
For cast iron,
r=n(soo-^)^|.
The extension of an external fibre and the reduction in area of cross
section corresponding to torsional strain are given in tables furnished
with the machine. For ultimate extensions the value of correspond-
ing to the maximum and not to the ultimate ordinate is taken.
10 5tV. — METALLURGY.
work together, as shown by the subsequent regularity of the
Hne.
At some point b the stress is relaxed, and the pencil falls to
some point c ; when the stress is re-applied, the pencil rises in
the line cb and continues nearly parallel to the straight por-
tion of the line Oa until it reaches its former height db.
The ordinates then slowly increase until, by the successive
rupture of the concentric fibrous layers, the curve terminates
at/
Note the total work Oabefg 0\ the elastic work OaL;
and the recoil dc and set Oc for the stress db. The parallel-
ism oi be to O'a shows the practical constancy of the co--
efficient of elasticity under varying stresses provided the total
elongation be diminished by the set. By some, this coefficient
is considered the most permanent physical characteristic of
steel, in various forms of which it has been found to vary less
than 8 per cent, in specimens whose elastic limits varied 200
per cent.
The point ^ is a new elastic limit, and the entire line may
be termed a locus of elastic limits. Of these the point a is
called the primitive elastic limit, and the other points various
special elastic limits. Notice that as these successively rise,
the potential work diminishes. The special elasticity thus
produced by stress, as distinguished from the primitive elas-
ticity of the specimen, is treated of in gun construction.
Some metals give a curve like //, in which it is difficult by
either of the methods given, page 3, to determine the elastic
limit. In such cases it is generally taken as the stress corre-
sponding to the point of tangency of a line inclined at 45°.
Graphical Representation of Special Physical Properties.
Considering the diagram, figure 9, to represent that of a
tensile instead of a torsional 'test, the principal properties of
the specimen are graphically expressed as follows:
The Tenacity, or the capacity to resist rupture by extension,
is measured by the maximum ordinate at e. The correspond-
XV. — METALLURGY. 11
ing Stress may be greater than that at which fracture finally
occurs. In such a case the form of the portion of the dia-
gram, ef, indicates probably the progressive rupture of the
final layers.
The Elasticity, or the property of resisting permanent exten-
sion or compression, as we have seen may be measured either
by an absolute quantity, the elastic limit, or by a rate. When
this rate is practically uniform, as in steel, page lo, the elas-
tic limit alone may serve to measure the elasticity.
The Ductility, or the property of submitting to permanent ex-
tension, may also be measured by an absolute quantity, O g,
or more exactly. Oh, figure 9; or by a rate. This rate- is
measured by the cotangent of the angle made by the tangent
to the diagram at any point beyond the elastic limit and the
axis of strains. This measure, although not generally
adopted, io important since it illustrates the phenomenon
known as the flow of metals under stress. As seen in the
following examples, this rate may vary not only in degree
but also in its sign.
Ductility, though useful in such arts as the drawing of
wire and of metallic cups like cartridge cases, is now regarded
only a secondary property of cannon metals. Cannon are so
proportioned that the elastic limit is the superior limit of the
applied forces, but the ductility of the metal is thought to
give an additional safeguard against destructive explosion.
But safety then depends rather upon the potential work of de-
formation of which the metal is capable than upon either its
tenacity or its ductility alone.
Particular Cases. 1. Woods.
To illustrate these remarks by reference to materials the
physical properties of which are more generally known than
those of the useful metals, the torsional diagrams of the prin-
cipal woods used in ordnance construction are represented
in figures 10, 11, 12.
The woods are arranged from right to left in the order of
12 XV.- METALLURGY.
their coefficients of elasticity. This brings them approxi-
mately in the order of hardness, or stiffness, black walnut
leading.
These qualities fit this wood to resist the abrasion to which
gun-stocks are subject, and to give to the easily bent gun-
barrel its necessary support.
The elastic limits of cypress and black walnut are seen to
be equal, but the cypress is much the tougher of the two. It
appears to be about equal to a poor quality of oak, for which
wood, in the construction of gun-carriages, it was formerly
used in localities where oak could not be procured.
The forms of the diagrams after passing the elastic limit
•are very characteristic. In some cases, as in ash and white
pine, the line continues for some distance parallel to the axis
of strains. This would indicate the use of these woods for
pieces which being long and slender are apt to be bent.
When lightness is an object, as in the former case for wagon
poles, sponge and rammer staves, agricultural-tool handles,
and in the latter case for building purposes, particularly of
railway carriages, the low density of these woods makes them
highly esteemed.
The sudden dip of dog-wood, oak, and hickory occurs in
most hard woods. It is supposed to arise from the lateral
slipping of the fibres, the cementing substance having given
way. When this is brittle, as in the resinous yellow pine, a
very sharp depression is sometimes seen.
In some cases, as in dog-wood, hickory, and notably in
elm, the line rises again, sometimes exceeding the elastic
limit. The rise is supposed to be due to the retwisting of the
fibres, separated at the elastic limit, into a consistent whole.
On the other hand, the step-like decline of some of the dia-
grams indicates the brittleness of the corresponding woods.
The surprising qualities of dog-wood show that the small
size of this tree is the principal bar to its utility.
The importance of testing machines is very imperfectly ap-
preciated among practical manufacturers. This appears from
XV. — METALLURGY. 13
one of the oak diagrams which was made by a piece taken
from a new gun-carriage the stock of which was broken in
two by firing.
2. Metals.
The diagrams in figure 13 will be referred to hereafter in
discussing the metals represented upon them. To avoid
confusion, curves of similar metals are arranged in groups, a
new origin for each group being taken along the axis of
strains.
II. ORDNANCE METALS.
The principal metals used in Ordnance manufactures are.
Ferreous. -
Steel I ^'^^'
' ( low. Cupreous or
Wrought Iron, Kalchoids.
. Cast Iron.
r Brasses,
Bronzes
and other alloys
of Cu, Sn, Zii.
Nomenclature.
For clearness of definition by scientific men, the forgeable
ferreous metals are proposed to be classified according to
their mode of manufacture and according to their capacity to
harden, and are designated as follows:
1st. Those made from a pasty mass, by the prefix. Weld.
2d. Those made by fusion, by the prefix, Ingot.
3d. Those which will harden and temper by the usual
treatment of steel, by the suffix, Steel.
4th. Those which will not sensibly harden, by the suffix,
Iron.
5th. The only unforgeable ferreous cannon metal is cast
iron, known in the crude state as pig-iron and after remelt-
ing, as castings.
This classification affords the following scheme;
14
XV.— METALLURGY.
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XV. — METALLURGY. 15
Relative Importance.
Owing to their peculiar adaptability to the demands of
construction, the ferreous ingot metals are gradually super-
seding all others, and the time when they will be altogether
employed except for subordinate purposes is delayed only by
our imperfect knowledge of their properties. These metals,
under the common name of steel, already cover in their
application the wide range between castings for the frames of
iron-clads, weighing many tons, figure 14, and horseshoe
nails, the successful making of which was formerly considered
the most severe test of the quality of wrought iron. The
ages of stone, bronze, cast and wrought iron have been suc-
ceeded by the age of steel.
On this account the following discussion will relate princi-
pally to steel. As a cannon metal it has only recently come
into favor, having been considered brittle and untrustworthy.
It is largely due to the patient genius of Krupp and Whit-
worth that this prejudice has been overcome.
As an example of the quality of modern gun steel may be
mentioned the fact that it was found impossible to break a
gun hoop under a drop giving a blow of nearly 100 ft.-tons,
the arrangement being represented in figure 15. Sixty or
seventy blows shortened the vertical diameter only half an
inch.
III. PROPERTIES.
The useful properties of metals have regard to their
1, Homogeneity,
I. Constitution.
{Jo be.)
I. Chemical as to i o' n
(2, Composition.
( 1, Homogeneity,
II. Physical as to -J 2, Structure,
( 3, Strain.
16 XV. — METALLURGY.
II. Capacity for
resisting.
{To do.)
I. Tensile j 1, Tenacity,
Stress, or ( 2, Ductility.
II. Compressive j 1, Incompressibility,
Stress, I 2, Hardness.
III. Either j 1, Elasticity,
Stress, or ( 2, Homogeneity.
III. Facility for being
worked.
{To suffer.)
C 1, Fusibility,
Hot, or \ 2, Weldability.
( 3, Malleability (also cold).
Cold, or 1, Annealability.
/. CONSTITUTION OF STEEL.
Metals should be homogeneous as to composition and struc-
ture so as to be homogeneous as to strain. Those which
have been fused are the most homogeneous ; but even they
may be imperfect, both chemically and physically, as follows :
I. CHEMICAL CONSTITUTION.
1. Homogeneity.
Pure iron can rarely be produced except by the methods
of the laboratory, and therefore in exceedingly small quanti-
ties. In practice it is combined with the most useful elements
by heat, the fusibility of the alloy usually increasing with the
number of elements contained. Fused metals in general are
imperfect alloys, the constituents of which tend to arrange
themselves according to their specific gravities. Due to the
property of liquation, certain of the most fusible alloys of
steel are found near the core of the ingot in greater propor-
tion than elsewhere. Thus, in a steel ingot the parts first
solidified represent most nearly its average composition, the
centre of the bottom being the softest and that near the top
the hardest, since the fusibility and the hardness of the alloy
increase with the percentage of C*
* Order of Oxidation.
Reactions during fusion depend so much upon the order of oxidation
of the constituents of pig-iron that the following approximate relation
should be learned:
XV. — METALLURGY. 17
The segregation of the Kalchoids is very objectionable.
2. Composition.
The following elements occur in iron alloys :
1. Carbon and iron as the principal constituents make the
steel best suited for general purposes. It has often been tried
to replace or supplement the action of carbon by other ele-
ments such as silicon, tungsten, chromium, nickel, etc., but
for general purposes carbon steel is far the most important.
As a rule, the greater percentage of carbon up to about
1.5 (and even 2 5 per cent.), or the higher the grade,
The more — The less —
1. hard and elastic ; 1. dense;
2. tenacious ; 2. ductile ;
3. brittle ; 3. weldable ;
4. fusible; 4. forgeable, does steel be-
5. expansible by heat, does come.
steel become.
The terms high and lotv referring to the grade of steel, or
per cent, of C contained, are loosely applied, but the tendency
is to draw the line at 0.35 per cent., where hardening by heat-
ing followed by rapid cooling becomes perceptible. The
following table exhibits the classification according to use.
So much depends upon the percentage of hardening constitu-
ents other than C, and upon the treatment of the steel in
manufacture, that the relation expressed is only approximate.
1. Silicon. 5. Iron.
2. Manganese. 6. Phosphorus, in presence of an acid
3. Phosphorus, in presence of slag; i. ^., one containing an
an oxidizing basic slag. excess of S i O^.
4. Carbon.
These and other following relations depend so much upon existing tem-
peratures and conditions that they are expressed in the most general terms.
18
XV. — METALLURGY.
Grade.
TABLE IL GRADES OF STEEL.
Per Cent, of Carbon. Application.
Low.
High.
Mild,
Hard,
Extra hard,
Tool,
Extra Tool,
Die,
Extra mild, 0.05 — 0.20 Boiler plates to be flanged,
bridge material.
0.20 — 0.35 Railroad axles, gun bar-
rels, etc.
0.35 — 0.50 Rails, cannon, etc.
0.50 — 0.65 Springs, saws, etc.
0.75 — 1.00 Chisels, cutters, etc.
1.00 — 1.20 Files and very hard tools.
2.50 Wire drawing, to resist
abrasion.
Carbon is generally supposed to exist in steel in two princi-
pal forms: 1. Cement carbon^ characteristic of annealed or
softened steel, and 2. Hardening carbo?i, characteristic of
hardened steel. The former is insoluble and the latter is
soluble in dilute H^ SO^. See page 48.
The following elements are admitted, either of necessity or
as Si physic ; i. e., replacing something more harmful or pro-
ducing a beneficial effect.
2. Silicon tends to displace C from combination, and to
confer its properties, although in a less degree.
It restores ''burned" or "rotten" steel by forming with
the particles of iron oxide, to the dissemination of which
this condition is often due, a fusible slag :
{Fe^ O^ + Siz=zFe Si O^ + Fe),
As Si increases the solvent power of steel for gases, and,
by reducing the iron oxide present in the hquid steel, prevents
the formation of CO it also prevents the honeycombing or
vesiculation of the metal from the ebullition of the gases
while the metal is becoming soUd.
If uncombined, Si O^ may remain as grit, which is injuri-
ous to the strength of the metal and destructive to cutting
tools.
XV. — MEtALLtJRGY. 19
When in excess, Si makes steel brittle. This is generally-
true of the non-ferreous ingredients of the alloy.
3. Manganese, unlike Si, tends to make C combine with
iron ; like Si, it tends to replace C functionally, but much less
energetically.
Afn resembles Si as a reducing agent, and forms with it and
iron oxide a very fluid, cleansing, slag.
The physical properties it confers vary with the proportion
present. With from 3 to 6 per cent,, the steel becomes very-
hard and brittle ; but with from 7 to 20 per cent, the steel
becomes very tough and strong.
Some Mn is necessary to prevent hoi-shortness, or the tend-
ency to disintegrate when forged, even when no 6* is present.
It also acts as an antidote to S, by forming Mn S, which is
insoluble in melted steel.
4. Phosphorus make steel cold short, or brittle at ordinary
temperatures. It can be removed only by some basic process,
as follows : Since the ordinary silicious, or acid, lining would
prevent the oxidation of P, and, by wasting the iron, would
increase the proportion in which P remained ; in the basic
process the furnace is lined with dolomite brick. Iron ore
and (for economy) limestone are added to the charge, so that
the phosphoric slag that is formed may continue basic.
The presence of Mn and Si in the pig iron from which
washed pig is thus formed, protects from oxidation the C that
it contains, and therefore maintains the fluidity of the charge,
until the Mn and Si are consumed. When this happens and
the bath boils with CO, the washed metal is cast into pigs
containing only about 0.1 of the original P.
So much C is retained that (after grading it by analysis)
the washed pig is easily remelted in further processes relating
to the manufacture of steel.
These processes permit the use of pig iron, which was
formerly too high in P.
20 XV. METALLtfRGV.
When added to the Kalchoids, P removes their greatest
enemy, oxygen.
5. Sulphur also is very difficult to remove, although the
hot-shortness that it produces may be corrected with Mn or
eliminated by Ca F^.
6. Chromium increases the hardness of steel without im-
pairing those qualities, such as ductility and malleability,
which are incompatible with the hardness resulting from high
carbon.
7. Aluminium is said to increase the fluidity of low steel,
and even of weld iron, in a remarkable degree, thus permit-
ting the metal to be cast without danger from vesiculation.
The fluidity of the metal in the mold permits the escape of
the occluded gases. Its action on iron oxide resembles that
of Si.
A new alloy known as Mitis metal, which is thus formed,
may be cast into the most complex forms.
8. Nickel remarkably increases the useful properties of
steel ; the result varying with the percentage as in Mn. The
armor plates now (1891) preferred are made of nickel steel.
9. Copper. When thoroughly deoxidized, steel may be
improved by the addition of Cu, although it is thought by
some that it makes steel hot-short,
II. PHYSICAL CONSTITUTION.
1. Homogeneity.
As in chemical composition, no fused metal is naturally
physically homogeneous, either in structure or in strain.
These properties may be so modified by after-treatment that
the following comparisons apply to non-forgeable metals as
ordinarily cooled after fusion ; and to forgeable metals when
annealed. This is the standard condition for their comparison*
2. Structure.
The structure is juaged of by the appearance of the frac-
tures; for exact comparison these should be similarly pro-
XV. — METALLURGY. 21
duced. By varying the method of breaking it, the fracture
of a bar of wrought iron may be made either crystalline or
fibrous within a few inches of its length.
Crystallization. It is assumed that ingot metals are crystal-
line, and weld metals fibrous, although the ultimate crystal-
line forms are doubtful.* Thus, the former may be supposed
to consist of normal crystals, and the latter of distorted crys-
tals cemented by a film of slag.
Normal crystals are supposed to be formed like those of
soluble salts ; the more slowly and quietly they are cooled
from fusion, the larger and weaker they are, and conversely.
(Bioxam, Art. 38.)
The crystalline axes are found perpendicular to the cooling
surfaces, so that surfaces of weakness are formed at the junc-
tion of inclined systems. See figures 16, 17. For this reason
the corresponding surfaces should be united by gradual curves
so as to distribute strains which would otherwise be localized.
Sharp re-entrant angles should be avoided in all structural
masses, even the non-crystalline.
Vesiculation. Another structural form arises from the oc-
clusion of air and other gases during the casting. This causes
^'' blow -holes,'' which increase with the viscidity of the fluid
mass. On the other hand, when the metal is free from blow-
holes, an axial cavity is formed, due to internal strain. This
is known as 3. pipe. Figure 18.
3. Strain.
Differences in the rate of cooling throughout a fluid mass
produce internal strain, the parts first solidifying being com-
pressed by their adhesion to the layers cooling subsequently,
which last are reciprocally extended. Similar effects follow
* By some the primitive structure of ingot steel is supposed to be that
of globules of the alloy imbedded in a mo e highly carbonized cement.
This is called the Cellular Theory.
22 XV. — METALLURGY.
unequal heating. The importance of this principle is fre-
quently apparent, particularly in dealing with iron castings.
//. CAPACITY FOR RESISTING STRESS,
Properties.
Owing to the facility of referring other stresses to a tensile
stress, this alone is generally considered, the incompressibiuty
of cannon metals being sufficiently guaranteed by their com-
bined hardness and tenacity.
The principal properties of 1. tenacity, 2. elasticity, 3.
ductility, and 4. toughness, have already been discussed.
5. Hardness is properly the property of resisting penetra-
tion ; combined with tenacity, with which it is almost invari-
ably associated, it renders cannon metal incompressible by
powder pressure, and in itself resists abrasion, erosion and
impact from hostile shot.
Steel may be artificially hardened by heating it, followed
by its rapid cooling. Steel and bronze may also be hardened
by their compression in a cold state ; externally by rolling
and internally by mandreling, which consists in forcing
through a hole conical plugs of slowly increasing diameter.
It is noteworthy that by heating and rapid cooling, brass,
bronze and the high Mn steel, p. 19, are softened,
III, FACILITY FOR BEING WORKED,
1. Fusibility.
This diminishes the number of joints in a given structure,
and, other things being equal, increases its cheapness, homo-
geneity and strength. Recent advances in mechanical en-
gineering have been principally due to the large units of con-
struction afforded by the capacity and power of modern
furnaces. Thus steel is replacing wrought iron, which is
formed by agglutination.
XV. — METALLURGY. 23
2. Malleability,
or to the power to endure hammering or roUing, particularly
at high temperatures, enables metals to be forged into special
shapes, thereby improving the quality of the metal and reduc-
ing the labor of finishing. When combined with fusibility,
it gives advantages peculiar to steel.
3. Weldability,
or the power of adhesion at high temperatures between
masses is characteristic of wrought iron and low steel. It is
upon this property that the manufacture of wrought iron
depends. This property in construction is inferior to fusi-
bility and hence is not utilized for steel except in small masses.
The process of electric welding is now (1891) successfully
employed. It consists in sending a powerful low-pressure
current through the abutting surfaces of the pieces to be
united. The resistance at the points of contact raises the
neighboring metal to the temperature of incipient fusion;
pressure being then applied, fresh surfaces are successively
brought into contact. Owing to the high temperature of the
first contacts, the current is mainly conveyed through the new
ones and so on until a homogeneous joint is formed.
Hollow projectiles are thus made from steel tubing welded
to a point and a base. It is even proposed to heat finished
pieces locally, so as to permit them to be bent or tempered
without injury from the hammer or the fire.
4. Annealability,
or the power to become soft, facilitates reduction to size by
cutting tools. All the cannon metals can be softened by
annealing, but to steel only can the necessary hardness be
restored, except mechanically.
Grindi?ig. It fortunately happens that hardened steel,
which can cut all the other useful metals, can itself be abraded
by grinding almost as easily as when soft.
24 XV. — METALLURGY.
This permits the change of form which often follows hard-
ening to be corrected by the use of either natural or artificial
grindstones. See Chapter XVII, page 14
CONCLUSION.
The relative standing of the five cannon metals may be
roughly indicated as follows :
^STEEL-> , IRON >
High, Low. Wrought, Cast. Bronze.
1.1 f?l^„aS'/1 ^ ^ 3 4 5.
t! 5 -( Homogeneity, I 1 o A. ^ f?
2 % I Hardness, normal, f ^ ^ ^ d o.
tn ^ 1^ Ductility, 4 3 15 2.
f Fusibility, 3 4 — 3
Malleability, 3 2 1 —
O cJ
cr
C (U
•^ § s( Weldability, — 2 1
Annealability or ^ ^ o q
variable hardness, f
This indicates why bronze and the irons, which, owing to
their workability, were until recently the only cannon metals,
are now obsolete.
IV. MANUFACTURE of the FERREOUS METALS.
/. CAST IRON,
Varieties.
The gray pig is known diS foundry or 77ielting irow, the white
pig as forge iron ; the latter is useful only for conversion
into wrought iron. Mottled pig is an intermediate variety.
Remelting.
To obtain strong castings, the foundry pig is ordinarily
remelted and run into molds of the required shape.
The specific gravity of pig-iron is about 7.00, and its
tenacity about 16,000 pounds to the square inch, but, when
remelted, the specific gravity is increased to about 7.25, and
the tenacity about doubled.
The remelting is effected in cupola or reverberatory fur-
naces, according to the kind of fuel available and the size
and quality of the casting required. It is always necessary
XV. — METALLURGY. 25
to melt as quickly as possible, and with the least consump-
tion of fuel. This usually requires artificial blast.
In Cupolas. The cupola furnace is generally employed ;
its size depends upon the amount of metal to be melted at a
time, and upon the kind of fuel.
A cupola extensively used is of the Mackenzie pattern, fig-
ure 19. It consists of the iody B, of elliptical cross section,
made of thick sheet-iron lined with fire-brick ; this is sur-
mounted by a conical hood H, terminating in the chimney C.
The blast is admitted through an annular tuyere extending
around the bottom part of the furnace. The charge is intro-
duced at the door D, and the molten metal, accumulated in
the hearth H, is drawn off at the spout S, and carried to the
mold through a channel or by means of ladles.
The elliptical section of the body in combination with the
annular tuyere increases the capacity of the furnace for a
given intensity of blast ; the object being to maintain a high
temperature in the vertical plane containing the transverse
axis of the ellipse, along which, for regularity of feeding, it
is desirable to cause the contents of the furnace to descend. I
The cupola furnace saves fuel, labor and time, and fur-
nishes a continuous supply of iron, which, since the carbon
in the pig-iron is not diminished by melting, is liquid and
therefore of the quality suited to foundry purposes.
The charge consists of pig-iron and generally scraps of
cast iron, a flux, and the fuel ; for the latter, coke and char-
coal are best, though anthracite is generally employed.
In Reverberatory Furnaces. Reverberatory furnaces are
principally used for the production of large castings, and are
specially adapted to all such as require great strength. Their
use is sometimes necessitated if the fuel at disposal contains
sulphur.
The name is derived from the arch which beats back the
flame on the metal to be heated.
The furnace, figure 20, is built of fire-brick bound strongly
together by iron bars or plates ; the hearih H is of refractory
S6 XV. — METALLURGY.
brick covered with a thick layer of Bre-sand ; the grate G is
large, that a great volume of flame from the fuel may be
drawn over the bridge -5 and through the furnace ; for this
purpose the chimney C is made very tall when no artificial
blast is used. The metal is introduced at the charging doors
D, D\ and, when melted, is drawn off" at the tap-hole (h).
The dimensions of the furnace depend chiefly on the charge
of iron and quality of the fuel. They are of correct propor-
tions if a nearly uniform temperature be produced in all parts
of the furnace.
Unlike the cupola, this furnace allows the iron to be kept
liquid for any length of time ; and, as the fuel is not in con-
tact with the metal, and carbon and silicon are removed by the
air, a stronger iron results. On the other hand, it does not
admit of constant casting, and involves a great loss of iron
by oxidation ; owing to these circumstances and to the greater
consumption of fuel, such furnaces are used only in large
foundries, and, whenever practicable, are replaced by cupolas
of large size.
Properties of Iron for Castings.
The color and texture of a casting depend greatly on its
size, and on the rapidity with which it has been cooled, and
upon its composition. As small castings cool quickly they
are almost always white, and the surface of large castings
partakes more of the quality of white iron than does the
interior.
When gray iron is melted, the particles of graphite to
which its color is due are dissolved by the liquid iron, and if
it be poured into a cold iron mold so as to solidify quickly,
the exterior of the casting will present much of the hardness
and appearance of white iron, the sudden cooling having pre-
vented the separation of the graphite. This is particularly
apt to follow the presence of manganese in the iron.
At the instant of solidification gray iron expands more
than white, giving a casting with sharp edges and a convex
XV. — METALLURGY. ^?
surface; and, as it subsequently contracts less, the initial
strains due to cooling are less.
White iron gives a casting with a concave surface, and
mottled iron one with a plane surface, the edges slightly
rounded.
SPECIAL CAST IRONS.
Malleable Cast Iron.
By extracting a portion of the carbon from cast-iron its
composition is assimilated to that of wrought iron and its
toughness increased ; the result is known as malleable cast
iron.
The castings to be softened are packed with powdered
haematite ore, or scales of oxide of iron, and the temperature
raised gradually to a red heat ; this is continued from three to
five days according to the thickness of the layer of malleable
metal required.
When withdrawn from the furnace, articles so heated have
the appearance of ordinary malleable iron, but are lighter
in color ; their fractured surfaces are white and finely granular,
occasionally having a silky appearance like that exhibited by
soft steel.
The principal application of this process is to such articles
as buckles, bits, stirrups, keys, etc.
Case-hardening. The stratum of malleable metal on the sur-
face may be converted into steel by the process of case-hard-
ening, which consists in a similar heating in contact with ani-
mal charcoal, after which, while still hot, the casting is plunged
into water or oil. This process is applied also to articles of
wrought iron, such as the parts of small-arms in which it is
desired to have a tough, somewhat soft interior protected
from friction or blows by a hard surface. The hammer and
breech-block of the Springfield rifle are so treated.
28 XV.— METALLURGY.
SPECIAL ALLOYS.
Varieties.
Spiegeleisen or Spiegel {Sp) and Ferro- Manganese (FM)
may be regarded as varieties of white cast iron alloyed with
a varying proportion of Mn, That which contains over 20
per cent, of Mn is known as FM. When Mn amounts to
80 or 90 per cent., it may consume by spontaneous oxidation.
The price of FM increases with its richness in Mn, for this
limits the choice of ores and increases the temperature of
reduction and fusion, and the loss by volatilization and oxi-
dation.
Silicon- Spiegel and Ferro-Silican are similar alloys, but con-
tain much more Silicon.
The following table exhibits roughly the ingredients of
some of the principal special alloys, and illustrates the state-
ments previously made as to the effects of Mn and Si upon
the proportion of iron in combination.
Note the gain in C as Mn increases, and its loss as Si
increases.
TABLE.
Name. 8% Mn C Fe^
(combined.) etc.
1. Ferro-Manganese, 80 7 13
2. " '* 60 6 34
3. Spiegel-Eisen, 1 10 5 84
4. Silico-Spiegel, 10 20 2 68
5. Ferro-Sihcon, 10 2 88
Use. /
These alloys are manufactured principally for the steel
makers, being used by them to improve the quality of steel
while in a state of fusion.
Generally speaking, Ferro-Manganese is used when the
quantity of C necessary is small as compared with the Mn
required ; and conversely with Spiegel-Eisen, although in the
XV. METALLURGY. 29
latter case C may be added directly in a pulverulent form, or
in a pure pig iron.
The Silicon irons are principally used to prevent vesicula-
tion; No. 4 is preferred to No. 5, as the increase in Mn
causes the Si to more thoroughly combine with the steel and
improves its structure.
//. MODERN MANUFACTURE OF WROUGHT IRON.
Principles.
The great cost of the hand labor engaged in the ordinary
process of puddling has led to the use of mechanical means
for accomplishing this result. The two principal processes
are those of Danks and Perfiot. Their common feature is
the continuous rotation, by mechanical means, of the vessel
containing the charge, thus avoiding the loss in time and
power due to the reciprocating action of the puddler's rabble ;
and diminishing the number of skilled workmen required.
The principle involved in these processes is that given in
Bloxam, Art. 219, viz.: That when cast iron is heated in con-
tact with iron oxide, the C and Si in the iron take O mainly
from the iron oxide in the fettling of the furnace. The C
passes off as CO and CO^, and the Si as an iron silicate or slag.
Danks Process.
The furnace, Figure 22, consists of a horizontal drum, revolv-
ing on rollers and lined with 2. fettling of lumps of haematite
ore set in a fused paste of the same ore. The flame from a sta-
tionary fireplace plays through one end of the drum and passes
off through a movable flue at the other end. The removal of
the flue permits the drum to be charged and emptied.
For economy. the furnace maybe charged with melted iron,
either directly from a blast furnace or from a cupola. If
charged cold the rate of revolution is slow while melting; it
is increased while boiling, during which the fettling and the
flame rapidly oxidize the C and Si exposed by the rolling of
the pasty mass and the adherent film and drip from that
30 XV, — METALLURGY.
which is melted. The drum is stopped to tap the cinder. It
is then revolved more rapidly than before, draining the pasty-
mass until it begins to ball. The large lumps, carried around
by adhesion, fall on those at the bottom and help to work out
the cinder. This is more thoroughly done afterward by the
usual methods.
Pernot Process.
The pan revolves under a stationary cover, on an axis in-
clined about 5° or 6° to the vertical, see figure 85. The fet-
tling is thus exposed alternately to the flame and to the metal,
the film of oxidized iron thus formed passing under the fluid
mass and assisting the reduction. Balling still has to be done
by hand ; but the process uses less coal than the ordinary
one, and the furnace can be more easily repaired.
These processes are losing their importance in consequence
of the rapidity with which steel of various grades is supplant-
ing wrought iron.
///. MANUFACTURE OF STEEL.
I. IN SMALL MASSES.
1. Weld Steels.
Puddled Steel. Puddled steel is made by stopping the pro-
cess of puddling when the de-carbonization of the cast iron
has sufficiently advanced. It is principally used for conver-
sion into other kinds of steel.
Blister Steel, which is made by cementation, being full of
fissures and cavities, is fit only for a few rough purposes, as
for facing hammers ; most of that made is used for conversion
into other kinds of steel.
Tilted Steel, When bars of blister steel are heated or
hammered into bars under a tilt hammer^ Figure 40, the pro-
duct is termed tilted steel ; spring steel is thus prepared.
Shear Steel. Shear steel is produced by cutting bars of
blister steel into convenient lengths, and piling, heating, and
welding them under a hammer, whereby is obtained a bar of
XV. METALLURGY. 31
uniform quality known as single shear steel ; the quality of
the metal is still further improved by a repetition of the pro-
cess, forming a bar of double shear steel. The oftener the
process is repeated, the more uniform is the resulting steel.
Shear steel is capable of receiving a better edge and a
higher polish than blister or spring steel; when well prepared,
it is not much inferior to crucible steel. It is very exten-
sively used in work where steel and iron have to be united by
welding, as in axe-bits and scissors.
2. Crucible Steel.
Although blister steel by repeated working under the ham-
mer acquires a tolerably homogeneous structure, it is still
further improved by fusion. The process, invented a century
ago, still remains in principle unaltered. Fragments of blis-
ter steel are melted in crucibles, figure 23, covered to exclude
the air, and the liquid poured into cast-iron ingot molds of
the shape and size required. These ingots usually contain
cavities; they are gotten rid of by heating the mass and ham-
mering it into coijipact and homogeneous bars.
Most crucible steel is now made direct from bars of the
best wrought iron ; they are broken and placed in the cruci-
ble with a small quantity of charcoal or pig iron, the amount
varying according to the grade of steel required ; some alloy
of manganese is subsequently added. The preliminary frac-
ture of the material charged facilitates its classification and
increases the uniformity of the product.
Properties.
In forging, crucible steel should never be raised beyond
a certain temperature, varying inversely with the grade,
or it will become brittle. It is difi&cult to weld, as it is usu-
ally high in carbon.
If a small quantity of manganese be added to the molten
metal, the steel will be more forgeable and may be welded
either to itself or to wrought iron.
32 XV. — METALLURGY.
Kemarks.
The manufacture of the weld steels and of crucible steel is
losing its importance, and crucibles are now principally used
for small masses in which the desired quality of the product
can, from the careful supervision exercised, be most easily
maintained.
The size of the crucible charge depends on the strength of
the melter and rarely exceeds 80 lbs. ; but with well drilled
men large numbers of such crucibles may be poured succes-
sively into a common ingot mold of any size. Krupp so casts
his large cannon, sometimes employing 1200 crucible bearers.
II. IN LARGE MASSES.
Processes.
The principal processes are the Bessemer and various forms
of the Open Hearth. Each of them has its province. The
former, owing to its rapidity, excels in cheapness, although
there is a loss of about 10 per cent, of iron ; the latter, owing
to its controllability, excels in quality. This takes time and
increases the cost by about 15 per cent., although there is in-
cidentally a slight gain of iron.
Carbonization and Tests.
Owing to the loss of iron from oxidation when completely
decarbonized, neither process is carried to an extreme, some
C being always left in the metal and its final percentage being
regulated by adding Sp or FM.
The percentage of C is judged of by the fracture ; by the
appearance of the nick required to produce fracture ; and
more carefully by a rapid color test, which consists in compar-
ing the color of a solution of the metal in dilute HNOg with
that of a standard solution. In the Bessemer process this in-
formation is applied to the next succeeding heat ; and in the
Open Hearth, as the operation is less hurried, to the heat itself.
Temperature.
The high temperature attained permits re-melting on the
spot of the scrap accumulating in all steel works, which would
3tV.— MEtALLURGV. 33
otherwise be of little value. In the Bessemer process this is
due to the oxidation of the Si in the pig ; in the Open Hearth
to the Siemens regenerator, which increases the temperature
cumulatively to a degree limited only by the refractoriness of
the furnace linings and the tendency of the gases to disso-
ciate. Thus, like many other inventions, the Open Hearth
process had to wait for the parallel development of some in-
significant art, i. e. that of the brickmaker.
Cranes.
The production of metal by both processes depends upon
the facility of manoeuvring large masses. Of the various pat-
terns of cranes used for this purpose. Sir Wm. Armstrong's
hydraulic crane, or some modification of it, is especially valu-
able in Bessemer practice. Its efficiency depends upon the
arrangement of peculiar valves which unite at a central point
called the ** pulpit" and which place the control of the whole
plant in the hands of one man.
For an Open Hearth plant, where frequently very heavy
masses must be moved and where the operations need not be
so rapidly performed, these cranes may be supplemented by
power swinging cranes or replaced by a traveling crane cover-
ing the whole building. The traveling crane consists of a
horizontal beam the ends of which roll on raised parallel
tracks. The weight hangs from a truck rolling on the beam
and may thus be transported to any point of the included
volume. This crane presents many advantages and is used
when the construction of the plant permits.
Casting Ingots.
In both processes, the melted steel is run from the furnace
into a ladle from which it is distributed by a crane into cast-
iron ingot molds.
Casting is sometimes done through an independent iron
gate entering the mold from below (Figure 24). The fluid
metal should enter in a quiet, solid stream so as to avoid
84 XV. — METALLURGY.
entangling air. This is best done by emptying the ladle into
the pool, from which it issues, mider a constant head, through
a cylindrical nozzle.
For gun work, the ingots are like Figure 25. The tong-
hold serves to attach the porter-bar in forging ; and the drum,
being girt with a sHng chain, permits the mass to be moved
about and turned axially under the hammer. The dotted
lines in Figure 25 indicate the form of the corresponding
sections of the ingot.
Ingots are cast at as low a temperature as possible consist-
ent with fluidity in order to diminish internal strain and to
save the inner surface of the mold, injuries to which may
imprison the ingot.
In order to fill the voids resulting from the shrinkage due
to internal strains, castings of all kinds are generally sur-
mounted by a smkifig head. This is a reservoir of the melted
metal, the cooling of which is often retarded by containing it
in a relatively non-conducting mold.
For economy of fuel it is generally sought to forge the in-
gots as soon as possible after they have solidified throughout ;
but, owing to interruptions in the work, the sequence cannot
always be maintained. Ingots may thus require re-heating ;
this should be gradual so as to avoid internal strain.
Fluid Compression.
Whitworth's method of fluid compression tends to obliter-
erate cavities by an hydraulic pressure of about 40000 lbs. per
square inch. A very strong steel mold provided with a por-
ous lining is employed. The pressure crushes down the vesic-
ulated shell first formed next to the walls of the mold, and
drives the fluid metal throughout the interstices. The lining
allows the escape of gas. By this means the ingot is reduced
about one eighth in length while cooling after casting. The
best results, however, are thought to be obtained by careful
melting and after-treatment of the steel while in a fluid state.
XV. — METALLURGY. 35
Bessemer Process.
(Figures 27—30.)
Varieties.
There are two general processes depending on the nature
of the pig-iron converted. If free from P, silicious or acid
linings may be used ; but if it contains much P, basic linings
are required. The former process, which is the more com-
mon, is here described.
Metal.
The iron must contain Si as a fuel, and hence gray pig, the
color of which is due to the carbon displaced, page 18, is
used. It should be free from P and S, as they are not re-
moved but, owing to the inevitable loss of iron, their propor-
tion is increased.
Main Operation.
The pigs are usually melted in a cupola and the fluid
charge, after weighing, run into the converter. A blast of
air is then blown down through one trunnion and up through
the perforated bottom and the fluid metal. The reactions
resemble those of puddling* and are principally due to the
heat evolved by the burning Si. This burns out the Mn and
C in the metal and, by forming ferreous slags, removes part of
the iron also. The fluidity of the metal is due to the inten-
sity of the heat ; the latter is due to the rapidity of the reac-
tion consequent upon the state of subdivision of the mass.
The burning Si raises the temperature and promotes the
fluidity of the bath more than does the C, because the CO
formed absorbs much heat by expansion and carries it off;
the slag remains and protects the bath from cooling. The
small portion of Mn present also acts as a fuel.
The basic process requires the blast of the Bessemer blower
* It has been said as an example of mechanical progress, that we
have replaced the laborious operation of the puUdler's rabHc by piercing
the iDolten metal by invigjble bars of air.
?56 XV.— METALLURGY.
to be prolonged after the C and Si in the pig have been re-
moved, the burning P maintaining the fluidity of the metal.
Periods.
Three periods are recognized, lasting as follows :
I. Three to five minutes, Si burning. The free C in the
pig becomes combined, in which state it is most easily oxi-
dized. The flame is feeble, with a hissing noise.
II. Six to ten minutes. The oxidation of C, principally
to CO, makes the mass boil with a thundering noise. A
yellow flame of incandescent particles is emitted at the nozzle.
III. Four to five minutes. The flame, principally of N, is
smaller, and of a pale bluish tint. In about 15 or 18 min-
utes from the beginning, the flame suddenly drops, showing
that the C is almost entirely gone. To save loss of iron by
further oxidation, the blow is then stopped as the converter is
turned down ; the carbonizer is then added by weight. If
Spiegel is used, it is melted in a separate cupola.
Final Operations.
The carbonizer preferred for low steel is FM, which, al-
though more costly than Sp, contains less C in proportion to
the Mn, so that enough Mn may be added to reduce the iron
oxide, combine with free O, and impart to the steel its char-
acteristic qualities without introducing enough C to make it
unduly hard. The production of FM is one of the improve-
ments for which this application of the process had to wait.
After standing for a few minutes, the contents of the con-
verter are poured into a ladle, the slag remaining in the vessel;
the slag is then emptied and the vessel turned up for a fresh
charge.
Remarks.
The melted pig may be conveyed directly from the blast fur-
nace ; but this is not often done, as it prevents the prelimi-
nary grading of the pigs by fracture.
The process is principally applied to the manufacture of
XV. — METALLURGY. 37
rails, for which it is sufficiently exact. The quaHty of the
product may be improved if time and waste are neglected and
the process carefully watched through the spectroscope.
The steps of the operation in the acid and the basic pro-
cesses, showing the rates at which the solid products are
oxidized and the proportions of the different gases succes-
sively formed, are represented in figures 28, 29, 30. In each
figure one scale is that of time in minutes from the beginning
of the blow, and the other represents the corresponding per-
centage of the special product in question. These diagrams
are the result of experiment.
/ Open-Hearth Process.
Varieties.
The hearth may be either of the stationary or of the rotary
type. In both cases the advantages of the process depend
upon the Siemens regenerative apparatus, which requires a
gaseous fuel.
The rotary hearth has the advantage of steam power and
of facility in making the repairs which the intense heat due
to the regenerative apparatus frequently requires. It is also
better able to dephosphorize pig-iron. The principal objec-
tion to it is the liability of derangement of the rotating
machinery ; but this can be overcome. Its process is here-
after described.
Distinctions were formerly made between the "pig and
ore " and the " pig and scrap " processes, depending upon
whether the melted pig-iron is decarbonized by the iron oxide
or diluted by the addition of scrap steel low in carbon.
Such distinctions are no longer important, as the former pro-
cess is generally employed.
The Siemens furnace with either the stationary or the revolv-
ing hearth is a mighty instrument for achieving various metal-
lurgical ends. Accordingly, many combinations are made in
88 XV. — METALLURGY.
its employment, pig-iron, washed pig, ore, fluxes, and, par-
ticularly for commercial products, scrap being added as
required or convenient.
Gaseous Fuel.
Advantages: 1st. Controllability, by which either an oxi-
dizing, reducing, or neutral flame can be uniformly obtained.
2d. Economy. 3d. Cleanliness. 4th. The accuracy with
which the low temperatures used in annealing ovens may be
estimated by the eye, the gas having been temporarily cut off
so as to obtain a background against which the true color of
Uhe heated piece will appear.
The gas may be natural or artificial.
Crude petroleum is becoming largely used as a fuel. Being
thrown into the furnace as a spray, it has many of the advan-
tages of a gas. It is also converted into gas by the action
of steam at a high temperature.*
Siemens Gas Producer.
This consists of a number of chambers united in groups of
four around a common stack E, figure 31. The stacks unite
in a common trunk which leads with a slightly downward
inclination to the valve box B of the furnace, figures 33, 34.
Each chamber is essentially a wedge-shaped funnel with one
inclined side terminating at the bottom in a grate B on which
the fuel is slowly burned. The CO^ formed, ascending
through the incandescent mass, becomes 2C0, and, with
other gases due to the partial distillation of the superin-
cumbent fuel, passes through the flue D to the stack E and
thence to the trunk, having in the trunk a slight excess over
atmospheric pressure to prevent leakage inward. The increase
* The oxygen in the H^ O combines with the carbon in the oil, forming
CO, and decomposing the hydro-carbons into new compounds richer in
H. The H derived from the steam combines with the new compounds,
and makes them still lower in the paraffine series. (Bloxam, Art, 320.)
XV. — METALLURGY. 39
of density due to cooling causes a gradual flow along the
trunk. The same effect can be obtained by using a blast
which gives more, better and hotter gas from fewer producers
burning poorer fuel than does the natural draft described.
Almost any kind of fuel from gas coal to sawdust may be
used, depending on the purpose in view.
The charging hopper A and the poker hole Care stopped
to prevent the escape of gas.
. Siemens Stationary Furnace.
(Figures32, 33, 34.)
Hearth.
This rests in a cast-iron basin T, beneath and around which
air circulates. It is enclosed in a rectangular box-like fur-
nace about 30 feet long, standing above the floor-line W, and
provided with the charging door U, and the spout V iox tap-
ping out the fluid charge.
Regenerators.
These are the essential parts of the apparatus and are
applied to many purposes in which high temperatures are
required.
The regenerator consists of four fire-brick chambers of
varying section, K; L ; M; iV, arranged in pairs. They
are filled with a crib work of loosely stacked fire-brick. From
each of the end chambers K^ JV, gas-flues S lead up into the
furnace ; and from each chamber Z, M, three air-flues P and
R lead up alongside the gas-flues to a point above their exit
in the furnace. This arrangement protects the metal from
oxidation ; and the roof, made higher than where reverbera-
tion is sought, from erosion by the flame.
Valves,
The gas, air, and reversing valves are shown in vertical sec-
tion (laid over a longitudinal section of the regenerators) in
Figure 32 ; in plan (laid over a horizontal section of the main
40 XV. — METALLURGY.
flues) F, G; Jy H in Figure 34 ; and in cross section in
Figure 33.
Operation.
Gas from the producers, regulated by the valve B, passes
down over the reversing valve C ; this is set so as to direct
the gas into the main flue F and the regenerator K, where it
percolates through the mass of hot brickwork and thence
passes at a high temperature into the furnace. Air is drawn
through the regulating valve F over the reversing valve C ,
through the main flue G into the hot regenerator L and,
passing up the flue /*, meets the hot gas as above described,
affording progressive combustion with intense heat.
After burning, the flame passes down the flues R^ S into
the other pair of regenerators J/, N^ which absorb most of
its heat. It then escapes through the main flues J, H under
the two reversing valves, and into the chimney flue AA' .
After about twenty minutes, K, L becoming cooler and M,
N heated, C, C are reversed by the handles D, when the
currents of gas and air are also reversed. The efl"ect of
reversal is cumulative, since to the heat of combustion is
added that which the gases absorb from the brickwork before
combustion. As the brickwork becomes progressively hotter,
the ultimate temperature attainable is independent of blast or
draught and is limited only by the refractoriness of the furnace
linings and the tendency of the gas to dissociate at high tem-
peratures.
Advantages.
The principal advantages are the high and uniform tem-
peratures attainable, with the other advantages due to the use
of gaseous fuel.
Employment.
When the furnace has been brought up to a melting heat,
the bottom is repaired with fire-sand and the charge thrown
XV. — METALLURGY. 41
in by hand. After melting, it is stirred with iron -bars and
treated as hereafter described in the Rotary Hearth,
Pernot Rotary Hearth.
(Figure 35.)
Hearth.
This consists essentially of a circular wrought-iron ' ^ pan "
lined with refractory material and mounted on conical rollers.
These run on a circular trough-shaped track mounted on a
carriage ; the latter rolls on two parallel rails on which it may
be run into and out of the stationary furnace chamber. The
pan is rotated by a circular-toothed rack beneath it gearing
into a toothed wheel or by an endless screw driven by steam
power. The pintle, which is hollow and contains a stream
of water, is incHned at about 6°, so as to bring the highest
portion of the hearth next to the door. In case of accident
to the tapping hole, more than one is provided.
The lining of the pan varies with the kind of work. For
ordinary melting it is of refractory siUcious material; but
where dephosphorization is sought by the Krupp process, the
lining is basic, preferably of lumps of refractory magnetite
set in a paste made of powdered haematite and iron scale.
The lower courses of the roof are then of dolomite brick.
Operation
For steel making, the charge, consisting of about 15 tons
of pig-iron free from P and 6", is thrown in through the charg-
ing door while the pan is revolving ; this distributes it auto-
matically. Further revolution of the pan then causes the
unmelted metal to dip into and out of the bath as previously
described for wrought iron. When the pig-iron is thoroughly
melted, rotation is stopped and ore is added at intervals,
each addition being followed by a violent ebullition of the
bath. Samples of metal or ''spoon tests'* are taken from
time to time and examined by the color test, the fracture, and
42 XV. — METALLURGY.
by the appearance of the nick made by the chisel at the
fracture. When the C in the bath is low enough, Si and Mn
are added to prevent vesiculation and to make the steel
malleable. The process is continuous, taking about eight
hours for a heat, with a variable interval for repairs.
Bepairs.
The hearth is repaired between heats by revolving it so as
to bring the portions most cut by the flame under a hole in
the roof through which material is thrown. The stationary
portion is repaired at about every twenty heats, the pan being
run out bodily on its carriage. This afl"ords a considerable
advantage, since in repairing the stationary furnace, time must
be taken to allow the mass of brickwork to cool down to an
endurable temperature ; owing to the lack of ventilation this
time may be very great.
V. MECHANICAL TREATMENT OF STEEL.
CASTING.
The successful casting of steel into final forms is still un-
certain. The principal difficulties arise from vesiculation and
internal strain Steel castings frequently replace iron forg-
ings of a low grade.
ROLLING
Rolling may be intended to produce forms either straight
or circular, and may be performed either hot or cold. The
latter has the special object of producing hard, polished sur-
faces of exact dimensions and is applied to iron or steel of
small sections only. The reduction is small.
Hot Rolling— Straight.
The following description of the rolHng of armor plate or
of structural steel is taken as a type.
The interior of a newly cast ingot is too liquid for safe
XV. — METALLURGY. 43
working, and by the time that this has sufficiently cooled in
the air, the exterior has become too hard. Consequently,
the cooling is often retarded in non-conducting soaking pits,
in which the initial heat of the interior and that which be-
comes sensible during solidification become uniformly dis-
tributed throughout the mass.
Or, if the ingot has become cold, it is brought slowly to
the proper temperature in a heating furnace. If this is done
too rapidly, the exterior may be over-heated before the interior
is at the proper temperature. The principle involved is of
wide application in the treatment of steel.
The universal mill consists of two pairs of massive rolls at
right angles to each other, so that one pair will roll the sides
of the ingot while the other pair rolls its top and bottom.
Each pair is driven by an independent steam engine. The
direction of the rotation may be rapidly reversed, and the
space between the members of each pair of rolls be rapidly
adjusted to suit the varying dimensions of the work.
A series of horizontal parallel rollers of small diameter,
independently driven, convey the ingot to and from the rolls,
and after rolling take it to the shears where it is trimmed and
cut into lengths.
These lengths, or blooms^ are often re-heated and re-rolled
by a mill trai?i into various structural shapes. For small work
the mill train usually consists of a series of rolls arranged in
sets of three, one above the other, or three high. They con-
tain grooves of appropriately decreasing section so that suc-
cessive /^i^i'<fi' reduce the bloom to the shape required. The
rotation of each roll is continuous, so that the piece passes
in one direction above the middle roll, and in the opposite
direction beneath it.
In roUing large sections the two-high system is generally
employed ; the rotation being reversed and the space adjusted
at every pass.
44 5tV.— MEtALLURGY.
In all large forgings great care is taken to cut out all visible
imperfections such as pulls^ which arise from deficient duc-
tiHty in the metal, and cold shuts, whicli are due to the folding
in of projecting portions at temperatures too low to admit of
their union to the mass.
Hot Rolling — Circular.
A small cylindrical ingot is flattened out or " upset " into a
"cheese" and punched from each side successively with a
conical drift. The punchings, or pieces cut out, usually con-
tain all the pipe. It is afterward hammered on the horn of
an anvil, figure 37, until the approximate forjji is obtained.
Then, being hung upon a fixed roller A, figure 38, another
roller B, independently driven at a higher rate of speed, is
raised by hydraulic pressure to the position shown by the
dotted lines. The thickness of the hoop is thus diminished,
and its diameter increased, since lateral spread is prevented
by the flanges a b which come in contact, each with the end
of the other roller. The process is used for making locomo-
tive tires and short hoops for guns. It tends to give a fibrous
structure to the steel, aff"ording great tangential strength.
WIRE DRAWING.
Operation.
This resembles rolling, except that the conical aperture in
the draw plate, figure 39, being stationary, the wire, previously
pointed and lubricated, is drawn through it by power, gener-
ally by being coiled around a revolving drum. Tubing is
similarly made, but large sizes, like gun-barrels, are rolkd as
described for rails, the sides being kept apart by an axial
mandrel which is stationary.
Effects.
The effect of wire drawing at low temperatures resembles
that of cold rolling in that it raises the elastic limit and tenacity
XV. — METALLURGY. 45
and diminishes the ductility of the metal so much that, if the
original section is much reduced, frequent annealing is nec-
essary. Steel wire has thus been given a tenacity of over
333,000 lbs. per square inch with an elastic limit half as high.
These qualities are especially adapted to the construction of
" wire-wound" cannon.
FORGING.
This includes the operations by which hot metal is ham-
mered into shape. It therefore requires furnaces, hammers
and anvils.
Furnaces.
For large masses modifications of the Siemens fupnace
called re-heating furnaces are now employed. These furnaces
are frequently served by a curved crane of the form shown in
figure 42. This increases the elasticity of the crane as against
the shocks due to forging.
Hammers.
For light work hammers may be of the vibrating class known
as //// or helve hammers, figure 40, in which a horizontal beam,
working on trunnions, carries at one end a heavy head ; this
is caused to rise and fall by the action of projections on a re-
volving wheel. Or they may be of the class known as drop
hammers, where a weight is raised by hand or by power and
allowed to fall upon the work after the manner of a pile
driver, figure 41.
But for heavy work steam hammers are used. They are
sometimes of the Single Acting type, figure 42, proposed by
Nasmyth in 1833. The inverted cylinder is mounted on legs
which spread sufficiently to allow freedom for the workmen.
The cylinder is usually traversed vertically by a heavy
piston-rod, to the lower end of which, sliding in guides
attached to the frame, is fastened a heavy head or tup.
Steam being admitted below the piston, it raises the hammer,
46 XV. — METALLURGY.
which is allowed to fall from any desired height. Its fall may-
be arrested by choking the exhaust by the automatic opera-
tion of the valves so that rapid rebounding blows may be
struck. See figure 43 and page 54.
Anvils.
The anvil with its foundations constitutes one of the most
expensive portions of a forge plant. The anvil of the 125-
ton hammer at South Bethlehem, Pa., copied from that shown
in figure 42, weighs about 1600 tons.
In order to avoid the effects of vibration, the foundations
of the anvil should be independent from those of the hammer.
The anvil proper, like the tup, is generally flat, but both
may be of various forms required by the shape of the work.
Small work is thus produced with great exactness by being
stamped between dies. The parts of small-arms and of other
machines made in great quantities, such as those for sewing
and for agricultural purposes, are thus very economically
forged into very nearly their finished sizes. When of hori-
zontally rectangular section, the anvil is generally set with one
of its diagonals in the plane of the legs, so as to give room
opposite all its faces for handling long forgings. Figure 43.
The energy on impact being the same, the action of a heavy
weight moving with a low velocity is preferred, as the efi"ect
is more penetrating and less local. This principle is utilized
in Condies hammer, in which, owing to the fact that the mass
of the cylinder is necessarily greater than that of the piston-
rod, the cylinder is made movable, the piston-rod being sta-
tionary.
The steam may be admitted above the piston, adding its
pressure to the weight of the moving mass. Such hammers
are Double Acting.
For small work a single support, figure 43, gives sufficient
steadiness and more room. The valve may then be worked
by a treadle under the control of the smith so as to give him
the use of both his hands. See figure 41.
XV. METALLURGY. 47
The local absorption of energy at the point of impact di-
minishes the reaction of the anvil, so that, as the thickness
of the work increases, the thoroughness of the forging dimin-
ishes. This requires frequent rotation of the work so that all
sides may be equally extended.*
For this reason Ramsbottam's duplex hammer is used, the
work lying between horizontal hammers moving with equal
and reciprocal velocities.
Anvils for hollow work. In forging hollow work, mandrels,
which are heavy solid cylinders passed through the forging,
are used in connection with the anvil proper. If supported
throughout its length by a V-shaped notch in the anvil, the
forging lymg in between, the mandrel is termed _/fj:^^/ if sup-
ported only and directly at its ends, the mandrel is called
swinging. Figures 44, 45.
The effect of forging is greatly affected by the way in which
the mandrel is used. Forging on a fixed mandrel extends
the work in length but does not sensibly affect the internal
diameter. Forging on a swinging mandrel increases both
internal and external diameters without affecting the length
of the work. Hence, the swinging mandrel is used for hoops
which are too wide for the tire-rolling machine.
Forging Press.
The defects in steam hammers above referred to will prob-
ably lead in time to a more general use of the hydraulic forging
press designed by Whitworth, Figures 44, 45. Its principal
advantage lies in the time during which the work is operated
on; this permits the molecular flow desired. t
* This is also true of rolling and limits the effective thickness of armor
plates.
t Opinions are divided as to the comparative merits of the hammer and
the press. The advocates of the hammer prefer it on the following grounds :
1. In forging solid work the effect of the hammer is greatest on the
exterior which is retained; and least on the interior, which for cannon
and heavy shafting is subsequently removed. The converse of this is
attributed to the press.
48
XV. METALLURGY.
VI. MOLECULAR TREATMENT OF STEEL.
The quality of steel depends upon :
1. Its composition.
2. Its structure as modified by heating and cooling.
1. Composition.
Pure iron and carbon make a typical steel. But other ele-
ments are of necessity present in all the steels met with in
practice.
Pure carbon steel is here discussed.
2. Structure.
Changes in structure from the effects of heating and quench-
ing steel appear to be associated with changes in its density
and also in the state of the contained carbon. What relation
exists between the change in state of the carbon and the
change in the structure of the steel is still uncertain.
States of Carbo7i.
Indeed, the precise nature of the states of the carbon,
although much experimented upon and discussed, is not
definitely known. As an indication of the uncertainty in
this matter, and also of the idea which most theories contain,
the following suppositions may be referred to.
The carbon is supposed by Professor Abel to be either in
the condition of an alloy, or of a diffused carbide. Another
chemist calls it diamond, or dissolved carbon. Others, and
the more recent authorities, waive this issue by calling it
** hardening " or " cement" carbon. See page 18.
Avoiding any specific hypothesis, we may designate these
states respectively as Fixed or Free, The former name, as
2. The prolonged contact with the dies of the press chills the forging,
the initial temperature of which therefore must be excessive ; while the
blows of the hammer are heating.
3. Hammering exposes superficial defects while pressing conceals them.
The 1 25-ton hammer, page 46, is intended for forging armor plates,
the quality of the surface of which is most important.
3tV.— METALLURGY. 49
the preceding nomenclature would indicate, corresponds to
the hard condition of steel, resembling that of white cast iron ;
and the latter to its softer condition, resembling gray iron.
See Bloxam, middle Art. 220.
BrinelVs Experiments,
Method.
The accompanying diagrams, Figure 46, are principally
based upon a long series of experiments made by a Swedish
engineer, J. A. Brinell, upon the changes in the structure of
steel due to heating it in diiferent temperatures and cooling it
at different rates. His results appear to agree well with those
of others. His method was :
I. To heat separate bars of the same steel, but of varying
structure, up to certain temperatures indicated by the color
of the hot metal,* and then to cool them in one of two ways :
1. Slowly in ashes, called herein cooling.
2. Suddenly in cold water, called herein quenching.
n. To examine a freshly fractured surface, the fracture
being similarly produced in all cases.
HI. To subject the steel after cooling or quenching to a
chemical test as to the state of the carbon contained.
Classification of Fractures.
The recognition of fractures, like that of colors due to cer-
tain temperatures, requires great experience, but the principal
fractures may be designated by symbols, as follows ;
Structure. Crystalline. Granular.
i Coarse, A. D.
Symbols. \ Intermediate, B. E.
( Finest, C. F.
Aspect, glistening, dull.
The most important is F, which may be called amorphous^
*The irisated colors in figure 46 are the chameleon tints of the
films of iron oxide of different thickness, which result when a
polished steel surface is moderately heated.
50 XV.— METALLURGY.
the crystals or grains being invisible to the naked eye. The
intermediate and various composite fractures described by
Brinell are not noted herein.
Characteristics of Fractures.
A, B, C, are relatively soft.
D, E, F, are relatively hard.
A, D, have low density (open grain) and are weak.
C, F, have high density (close grain) and are strong.
Therefore, C has softness and strength ; it is extensible.
This fracture is sought in annealing.
Therefore, F has hardness and strength ; it is inextensible.
This fracture is sought in hardening.
F has the maximum density.
DIAGRAMS.
Explanation.
Figure 46 illustrates the changes in structure and state due
to heating and either cooling or quenching the steel experi-
mented on by Brinell. The axis of each diagram intersects a
common scale of temperatures which, for any particular grade
of steel, are indicated by the accompanying colors.
The temperature W is critical in its effects on structure and
state : it is the only high temperature at which, without having
been exceeded, if steel be que7iched, the resulting fracture will be
amorphous, F. The lower the grade of steel, the higher is the
temperature corresponding to F, and conversely. The cor-
responding color must be determined empirically for each
grade, and, for important work, even for each ingot of steel.
The steel used by Brinell had about 0.50 per cent, carbon,
such as is used for cannon.
Each diagram represents a group of experiments upon bars
in which the same structure had been previously produced by
the methods indicated above. An ordinate along the axis
represents the temperature to which a piece of steel was
heated ; the abscissa to the left represents roughly the result-
XV. — METALLURGY. 51
ing coarseness of structure. The character of the structure is
indicated by reference letters. The extremities of abscissae
so determined are connected by a line indicating whether,
after heating to the desired extent, the bars were quenched or
cooled.
'Quenching is represented by a full line .
Cooling is represented by a wavy line'-^^_^'^,^_^'^.^^ .
The dotted line to the right of the axis represents roughly
by its abscissae the state of the carbon at different temperatures,
its relative freedom being represented by the corresponding
abscissae of the dotted hne.
Interpretation.
Study of the diagrams will show that — •
At W quenching always gives F and fixes carbon.
At W cooling always gives C and frees carbon.
Below W the crystalline structure does not change.
Below W the granular structure gradually becomes finer.
Below W the amorphous structure gradually becomes
coarser (the only change possible).
Above W all structures gradually become coarser, being
crystalline if cooled, and granular if quenched.
The change of carbon from free to fixed is sudden and is
called hardening.
The change of carbon from fixed to free is gradual. If
partial, it is called tempering, and if total, it is properly
termed annealing.
Crystalline structure is associated with free carbon.
Granular structure is associated with fixed carbon.
Conclusions as to the Treatment of Steel.
1. After forging a cutting instrument or spring, it must be
hardened so as to fix the carbon, as a necessary preliminary
to its gradual release by tempering.
2. In tempering hardened steel, the less it is heated the less
52 XV. — METALLURGY.
is its structure affected; and the less is the change in the
state of the carbon.
8. The fixed state is the more stable, so that it takes time
to change it throughout the mass without exceeding the de-
sired temperature externally. Such an excess would affect
the structure of the over-heated parts. The metallurgical
term soaking aptly illustrates the manner of heating steel
from which the best results are obtained.
The effects due to a given temperature may, however, be
produced by exposing the steel to a lower temperature for a
longer time than usual. Many of the following apparent
exceptions to the general rules appear to depend upon the
question of time.
4. The carbon having been freed by slow heating, the rate
of the cooHng below W is indifferent unless the mass of the
piece be so great as to cause the structure to change from the
prolonged action of its internal heat.
5. If W be exceeded the effect on structure of hardening is
lost, and the steel must be cooled below W and re-heated to
W to refine it.
Use of the Term, Temper.
Much confusion has followed the loose use of the term
temper. Besides being applied to the grade of steel, it is also
commonly used to indicate hardening; whereas we see that —
Hardening is produced by quenching at W and fixing the
carbon.
Tempering is a mitigation of the hardness above produced
which follows from subsequently heating steel to some tem-
perature below W, the proportion of the carbon thus freed
depending on the temperature attained. Whether the steel
should then be cooled or quenched depends upon the mass
of the piece. It is usually quenched.
Annealing properly consists in cooling at W so as to free
all the carbon possible and to destroy the effects of harden-
X'V. — METALLURGY. 58
ing. But it is also a term commonly applied to the cooling
below W of steel, whether previously fully hardened or not.
According to the temperature attained and to the time taken
to cool the piece, it is softened and freed from internal
strain.
Bate of Cooling.
The brittleness and the hardness of steel will be increased
by increasing the rate of cooling from W, either by quench-
ing in mercury, or in water the conductivity of which has
been increased by acidulation or by the solution of a salt.
The same effect is obtained by using water at a low temper-
ature, or by frequent changes of the particles in contact, by
motion either of the metal or of the water.
By reducing the rate of cooling as by the use of oil or
tallow, the effect known as oil hardening is produced. Its
effect is intermediate between C and F, and is probably largely
mechanical, the sudden cooling of the external layers prevent-
ing the expansion of the internal mass during subsequent
attempts at crystallization. This limits the size of the crystals
formed and increases the strength of the metal; but it pro-
duces some internal strain which may be relieved by temper-
ing at a low heat. The charred oil next to the surface, like
the scale, tends to delay cooling.
EFFECTS OF FORGING,
Above W.
Except when in small masses steel is generally heated above
W in order to give it the plasticity required for forging. In
this case the crystals are not supposed to be destroyed but to
be softened and expanded by the heat. Having been further
disturbed by the hammer, they are supposed on cooling to
assume the sizes and shapes due to the temperature at which
they have been worked, with intervals between the crystals
depending on the treatment received. Free crystallization
thus implies porosity and a diminished density, which is
further diminished by heavy forging at a high heat.
M XV. — METALLURGY.
Owing to the tendency of the crystals to shde over their ad-
jacent surfaces, a heavy blow may cause the fracture of over-
heated steel. It may indeed fall to pieces in the fire. But,
if such steel be lightly and rapidly hammered over its entire
surface, the effect will resemble that due to agitating a crystal-
lizing solution (Bloxam, Art. 38), m the reduction of the size
of the crystals and in the increased strength of the material.
This effect having been attained, further forging at a lower
temperature tends to form the piece and to distribute locally
any cavities which may exist.
In forging gun work the ingot is reduced in thickness about
one-half; the reduction being greatest for those portions of
the gun that lie nearest to the bore.
Wa/er Annealing. Owing to the difficulty of penetrating
large masses of metal by the vibrations of the hammer, the
greater part of the metal treated as above will be, when cooled,
like A or B or a combination of both. When the size of the
piece permits, one remedy proposed is to re-heat slowly to W,
to quench so as to prevent free crystaUization, and, as soon
as the temperature falls sufficiently below W, to remove the
steel from the water and allow it to cool slowly in air. See
Diagrams IV and V. The internal heat removes internal
strain. Railway axles are thus treated, the process being
called "water anneaUng."
The structure of a steel casting may be improved by heat-
ing it to W and cooling it slowly.
Forging Below W.
When the hammer is of sufficient power, the best effect will
be attained by forging just below W. The crystals are sup-
posed not to be much expanded by this heat ; but, being
softened, they may be compacted so as to destroy the porosity
due to free crystallization. This treatment gives the highest
density attainable, viz., 8.0; the steel resists the file, has a
XV. — METALLURGY. 6B
waxy fracture, and yields a beautifully veined surface when
etched.* This work requires hammers of great power when
large masses are thus forged.
The experience of all steel makers tends to show the ad-
vantage of forging at as low a temperature as possible. Work-
men incline to over- heat the steel so as to diminish their labor,
— but this should be avoided.
A very fine quality of steel wire made in England by Stubbs
and much used for making drills and fine tools is said to be
made by being forged between semi-cylindrical dies by a light
"pony" trip-hammer running with very great rapidity. The
temperature required is attained by the hammering.
INTERNAL STRAINS.
These arise from differences in the rate of cooling through-
out the mass, being increased in large masses by the deficient
conductivity of hot metals. It thus requires much experience
to judge of the internal temperature from the appearance of
the outside of the mass.
These strains increase with the maximum temperature at-
tained, being greatest in the ingot.
They also increase with the area of cross section of the mass,
so that it is well to defer the hardening until the pieces are as
nearly as possible of their finished dimensions.
Uneven forging produces "hammer strain" which is re-
Heved by annealing.
Difference in section causes differences in rate of cooling,
so that it is well to quench the thicker portions of irregular
masses first.
Other things being equal, internal strain increases with the
grade of steel.
* This is probably the original Damascus steel, which has been imitated
by the moderns by twisting together and welding wrought iron and steel
as in shot-guns.
56 XV. METALLURGY.
VII. GUN CONSTRUCTION.
I. BUILT-UP GUNS.
The operations are substantially as follows :
Casting Ingot.
For forgings such as tubes and jackets the ingot is often
cast square, as shown in Figure 25. For short pieces like
hoops, it is sometimes cylindrical. In order to obtain solid
metal and to free it from slag, sand and other impurities a
given amount of the top and bottom of each ingot is cut off
and discarded during the process of forging.
The ingot is sometimes cast hollow. But this is objection-
able, for it transfers the unsoundness found in the centre of a
solid casting to the middle of the walls of the gun.
Coring.
The ingot may then be trepanned by a sort of cylindrical
saw by which a solid core is removed. This rapidly removes
the more porous portions of the ingot, which are in a more
valuable form for minor purposes than the shavings from
ordinary boring. This operation sometimes precedes and
sometimes follows the forging, depending upon what tools the
plant affords and also upon the size of the gun.
Forging.
For solid ingots the work is constantly rotated during
forging by means of the porter-bar, which is a long handle
clamped to the tong-hold. A sling chain around the drum
forms a fulcrum. Man or steam power is used according to
the size of the work.
Cored tubes and jackets are forged on a fixed mandrel to
approximately their finished dimensions.
Blanks for hoops are cut off the ingot and upset, or hammered
lengthwise into a cheese-like form. After punching they are
treated as described page 44, or, instead of rolling, they are
XV. — METALLURGY. 57
forged on a mandrel. The choice of operations depends on
the length of the hoop and the facilities available.
After every operation the piece is carefully chipped by hand
to remove/////?, seams and cold shuts.
Treatment and Tests.
The term treatment applies to the methods employed to
affect the structure of steel, viz., annealings hardening and
re-annealing. The sequence of the tests is important.
The *' hammer strain" is relieved by annealing. Annealing
also facilitates the reduction by cutting tools to the rough-
finished sizes required for oil-hardening.
After annealing, tests of the metal are made to discover its
characteristics, and thus, to a certain extent, to regulate its
subsequent treatment.
The pieces are then rough-bored and turned to nearly their
finished size.
They are afterwards oil-hardened (generally called "oil-
tempered") by being uniformly heated to W in a furnace
constructed with reference to the shape of the heated piece,
e.g. tubes in a vertical flue, through many ports in the sides
of which flame enters tangentially and hoops in an ordinary
low furnace. Each piece is then immersed with its axis
vertical in a large tank of oil, holding many tons.
The tank is surrounded by a jacket through which a stream
of water flows with required velocity. The oil is also caused
to circulate by suitable arrangements.
The pieces are re an?tealed * to remove the internal strain
due to hardening. For this they are slowly heated to a low,
red heat and allowed to cool very slowly. This heat improves
the structure, but may slightly reduce the strength of the
metal.
* This is properly tempering.
XV. — metallurgy;
Tests of the metal are again made to see if it fulfils the
necessary requirements.
Assembling.
The parts are then turned and bored to finished dimensions
and assembled by shrinkage, the interior diameter of the out-
side cylinder to be assembled being finish-bored to the diam-
eter prescribed for the contact surface, and the exterior diam-
eter of the surface upon which it is to be assembled being
turned to the excess prescribed for the shrinkage. The eff"ect
of the shrinkage, which follows the heating of the outer
cylinder so that it may pass over the inner one, is sometimes
to bring the surfaces in contact within the range of molecular
cohesion. This phenomenon may sometimes be seen even
between cold bodies. When the steel plugs, used to gauge
the calibre of small-arms, being chemically clean, enter forci-
bly a clean bore, they are sometimes lost through ''freezing."
The hoops are secured by being screwed together, but
preferably by interlocking projections that slip by each other
when expanded by heat, figure 47.
The policy of our government with regard to gun con-
struction has been to obtain from private manufacturers the
forgings rough-bored and turned, and to finish and assemble
the various parts in its own shops.
IL STEEL CAST GUNS.
Objections.
The economical advantages of this process, which consists
in making the gun of a single steel casting after the manner
formerly adopted for cast-iron guns, are off'set by the follow-
ing objections:
I. Mechanical.
1. The enormous increase of the masses to be handled due
to the weight of the sinking head, which, unless its functions
can be replaced by other means, may weigh almost as much
as the ingot itself.
XV. — METALLURGY.
A Steel-cast gun weighs, in the rough, about 3 times as
much as the heaviest ingot required for a built-up gun of the
same calibre.
2. The difficulty of making molds strong enough to retain
the high columns of metal required by modern powder.
3. The loss in cutting up the sinking head, for re-melting
or in disposing of failures.
II. Constitutional.
1. The vesiculation, impossible to correct by forging.
2. The effect on crystallization due to slow cooling, also
impossible to correct by forging.
3. The segregation of elements of different densities in
cooling.
4. The internal strains developed in cooling castings which,
for the heaviest guns, cast hollow, would possibly be 60 or
80 feet high, with walls 3 or 4 feet thick. If cast solid, this
thickness would be increased.
Remark. This class of objections may possibly be over-
come with increased experience in the treatment of the fluid
metal, and by annealing the gun after casting.
Such experience must be costly, for it can be acquired
only by dealing with masses approximately as great as those
of the guns themselves.
III. Structural.
1. The impossibility of making physical or chemical tests
of internal specimens.
2. The impossibility of adapting the composition of con-
centric parts to their specific functions by the principle of
*' Varying Elasticity," to be hereafter discussed.
3. The neglect of the principle of "Initial Tension" by
which the inner parts may, by preliminary compression, be
prepared for the strain of extension on firing. This principle
is ilhistrated when a blacksmith shrinks on a tire.
IV. Historical.
1. Krupp's original guns, which were massive forgings,
CO XV. — METALLURGY*.
have been gradually replaced by guns of increasing com-
plexity of structure.
2. The only recorded failures in built-up guns have occurred
in the large masses constituting the tube ; sometimes when
unsupported, as in the chase; or when imperfectly supported,
as when a steel tube was surrounded by a jacket of ductile
wrought iron. This, having been expanded beyond its elastic
limit, failed to support the tube, which, on further firing,
cracked.
XVI. — PROJECTILES.
CHAPTER XVI.
PROJECTILES.
Definition.
Functionally speaking, a projectile is a vehicle for the
transfer of energy to a disconnected object.
The energy transferred may be wholly kinetic, as when
the projectile acts by impact only. It may be wholly potential,
as when the kinetic energy of the envelope of the mass may
be neglected in comparison with the potential energy of its
contents. And it may be of both kinds, as when the kinetic
energy of the envelope is considerable.
SECTIONAL DENSITY.
On account of the work done on the intervening resist-
ances, the energy actually transferred to the object will
always be less than that originally imparted to the projectile.
The resistance to penetration offered by the intervening
medium and the object, other things being equal, varies
directly with the area of cross-section, a^ at right angles
to the trajectory. Let us call, d, the diameter of the circle
whose area is, «, and F=f—- — the total resistance causing
retardation.
The retardation, which for a given projectile is propor-
tional to the loss of energy per unit of path, will, for differ-
ent projectiles meeting the same resistance, vary inversely
with the mass of each projectile; or, calling;
XVI. — PROJECTILES.
p, the retardation in the direction of the axis of Xj
M, the mass of the projectile;
E, the energy in the direction of X;
we have, neglecting variations in g; —
_dE \ _gp7t d"^ _ d^
^~"d^"M~ ~T~ 'W^W* (-^^
in which k, is some function of the pressure per unit of area,
/, which pressure will vary with the veloucity, the meridian
section and the nature of <^he surface of the projectile.*
d^
The ballistic coefficient^ or coefficient of retardation ^2,^ -—
is called, may therefore be used to compare the inherent
capacities of projectiles for retardation; and the reciprocal
W
of this expression, or —-^ which is called the j-^<r//^^/dr/^<?;zj/(>',
may be used to compare their inherent capacities to over-
come resistances. In English measures ^is taken in pounds,
and d in inches.
VARIATIONS IN SECTIONAL DENSITY.
Causes.
The sectional density of a projectile may be increased as
follows: —
I. If the dimensions are constant, by increasing the mean
density.
II . If its mean density is constant, by varying its dimen-
sions, viz. : —
* Since the form and dimensions of a projectile are independent of its
velocity, and since the effect upon p of variations in the meridian section
and the nature of the surface is small compared with those which result
from changes in its diameter and weight, and disappears when similar
projectiles are compared; we may for the present consider, k, for any pro-
jectile as constant, so that the value of p may be considered to vary only
With the relation between d^ and W%
XVI. — PROJECTILES.
1. If its proportions are constant, by increasing its calibre;
since w varies as d^^ while a varies only as d}.
2. If the calibre is constant, by increasing the weight.
3. If the weight is constant, by decreasing the calibre.
All these changes virtually lengthen the projectile.
Effects on Flight.
Increasing the sectional density of a projectile which has
a given initial velocity increases its range and penetration,
since the loss of energy over a given path is diminished. It
may also increase its accuracy, since the time of flight over
a given path, and therefore the effect of various perturbat-
ing causes may be diminished. The penetration is still
further increased by increasing the indeformability of the
material of which the projectile is composed, so that the
work of deformation on impact may be done rather by the
projectile, than upon it.
But, owing to the non-coincidence of the centers of mass
and of the area exposed to the resistance of the air,
during the flight of an oblong projectile a couple is formed
which tends to cause the projectile to tumble or revolve
about a transverse axis. This diminishes its sectional den-
sity and makes it variable. Such projectiles are therefore
given the rifle motion, which impresses upon them sufficient
angular velocity about the longer axis to make this a stable
axis of rotation, and therefore to make their sectional den-
sity constant and a maximum. The same reason applies in
a less degree to spherical projectiles, in which the centres
of mass and of figure can rarely be made to coincide.
Effect upon the Gun.
Increasing the length of an oblong projectile increases
its tendency to tumble, and hence requires a greater energy
of rotation. This diminishes the kinetic energy of transla-
tion due to the conversion of a given charge. In a certain
XVI. — PROJECTILES.
sea coast rifle the rotary energy amounts to about 0.01 of
the total muzzle energy.
Also, since increasing the sectional density increases the
mass to be moved per unit of sectional area, a given accel-
eration requires an increase in the intensity of the gaseous
pressure per unit of area. Therefore, since V=/adt, to
obtain a given initial velocity with a projectile of which the
sectional density has been increased, the stress upon the
gun must also be increased unless special provision be made
by the methods indicated in Chapter XI.
Owing to the weakness of cannon in use when the rifle
principle was first applied, the increase in sectional density
required a reduction in the initial velocity; this, although
compensated for by greater accuracy and longer ranges,
caused the initial portions of the trajectory to be more
curved than with the spherical projectiles formerly em-
ployed. See Chapter I. Consequently, the general adoption
of oblong projectiles was delayed until the necessary im-
provements in the gun and its ammunition had been per-
fected. See Chapter XIII.
Comparison of Forms.
Although the oblong form is universally employed in new
constructions, the following comparison illustrates some of
the reasons influencing and opposing the change of form.
Advantages of Oblong Projectiles,
The form, capacity and sectional density may be altered
indefinitely, with the advantages noted in the text. The
following incidental advantages also exist:
Projectiles of the same caliber, but of different natures,
or mean densities, may be made of the same weight; so that
they may be fired at the same ranges with the same angles
of projection.
XVI. — PROJECTILES.
The oblorg form facilitates the operation of fuzes which
act by impact; since the poinf-. and direction of the impact
can be predicted.
Disadvantages of Ohlofig Projectiles.
The centers of mass and of pressure do not coincide;
they are more expensive; the liability to injury of the soft
metal device by which they are rotated requires greater
care in their transportation and may interfere in their
loading; in ricocheting over land or water their rebounds
are much less certain and regular, both in altitude and
direction. The rotation of rifled projectiles of the explosive
class tends, upon bursting, to scatter their fragments unduly
beyond the plane of the trajectory. The curvature of the
trajectory at short ranges is increased.
MATERIAL.
The principle of sectional density mainly determines the
selection of the proper material for a projectile, with regard
to its behavior in the gun, in the air, and upon the object.
Its application is so apparent that only a few of the minor
properties of the materials employed will be mentioned.
Stone was employed originally in catapults and continued
to be used in cannon by the Turks as late as 1807.
Lead is suitable for use against animate objects only, since
in large cannon it is disfigured and even partially melted.
Wrought Iron in large masses is expensive, as it requires
welding and forging; it is also too soft.
Cast Iron was until recently exclusively used for artillery
projectiles on account of its fusibility and its small original
cost. When cast in molds, so that the point cools in con-
tact with a cast iron chill, while the body cools more slowly
in sand, its local hardness, crushing strength and density
are greatly increased, without causing brittleness in that
XVI. — PROJECTILES.
portion cooled in the sand. Against the wrought iron armor
formerly employed, such projectiles are indeformable; but
they are pulverized against the steel-faced and chilled iron
armor of the present day. For ordinary purposes cast iron
is still generally employed.
Steel possesses all the qualities required in a projectile,
but is costly. It is used in two forms, both of which are
usually oil-tempered.
1. Forged; including for special purposes, rolled or drawn
steel tubes. This form of steel, especially when alloyed
with chromium, is so far the best, but the most costly. A
9 inch Whitworth forged steel shell, costing $100, or 12
times as much as a similar projectile of chilled cast iron, has
been fired three times through wrought iron 12 inches thick.
2. Steel cast projectiles have, owing to their greater cheap-
ness, been much experimented with; but, for the reasons
given in Chapter XV, have so far proved inferior to those
that are forged.
SPHERICAL DENSITY.
W
Since the sectional density, -— , of similar projectiles in-
creases with the caliber, if we divide the sectional density
W
by the caliber we shall obtain a constant, -73-, which expresses
the weight per unit of volume of a cube whose weight is
equal to that of the projectile and whose height is equal to
the diameter of the bore. This is taken as the measure of
the spherical density of the projectile.
Since all spherical solid shot of the same material are simi-
lar, their spherical density is constant, and may therefore be
taken as the unit by which to measure the spherical density
of oblong projectiles of the same material.
Expressing the spherical density by S^ and the weight in
XVI. — PROJECTILES.
pounds of a unit of volume of the material by S, we have
for a spherical solid shot, of which the volume is F,
(7)'-
ci^ d' ~3 \d J ~ 3 8*
For projectiles made of iron, 6 may be taken as % pound,
and 7t may be taken approximately as 3.0; therefore
^., _ _ _ c,
and for an oblong iron projectile in terms of S^^,
^ _W' 1 _ 8 W
S^i, therefore, expresses the effective increase in density
that arises from elongating the projectile.
We might proceed similarly with other materials having
different values of 6; but it is convenient to retain iSg} as a
common standard; so that, in general terms, S may be taken
to measure the number of times that the mass of the inscribed
solid iron sphere is contained in that of the projectile con-
sidered.
Unless the caliber be fixed, the spherical and sectional
densities of projectiles vary independently of each other.
The spherical density of the first oblong projectiles used in
cannon in 1859, was about 2.0; but recent improvements in
guns, powder and projectiles have increased it from about 3.0
m 1880, to about 4.5 in 1887, the muzzle velocity not being
correspondingly reduced.
If all projectiles made of the same material had the same
mean density and the same form, their spherical densities
would be a function of their lengths. But as such is not the
case, their length is independently stated, generally in cali-
bers. In fact, the caliber is getting to be taken as the general
unit of measure of all the linear dimensions relating to the
interior of the piece.
dim'B.t^'
XVL — l^ROjECTtLEg.
Corollary,
Referring to the discussion on page 7, we see that the
weight in pounds of a sohd spherical cast iron projectile is
very nearly equal to the cube of its radius in inches. This
affords an easy method of approximating to the weight of
an oblong projectile when the type of gun from which it is
to be fired is known.
RIFLING.
History.
The invention of rifling by Gaspard Zoller of Vienna is
said to have been made soon after the discovery of America.
The first rifle grooves were made straight, and intended only
to facilitate the loading of tightly fitting bullets. The advan-
tages of the spiral groove, which were accidentally dis-
covered, were not applied to oblong projectiles, even in small
arms, until about 100 years ago, at which time the subject
was thoroughly discussed by the eminent mathematician
Eobins. It is worthy of remark that to Robins we owe the
first practical apparatus for the measurement of the velocity
of projectiles; a pendulum into which the projectile was fired,
and from the nwDmentum of which that of the projectile
could be computed.
The general adoption of the rifle principle for small arms
was retarded by the difliculty found in loading the rifle: this
w^as generally accomiplished by the blows of a mallet on a stout
iron ramrod. For cannon, attempts were made at an early
date and are frequently renewed, to impart the rifle motion
by the action of the gas, or of the air upon spiral grooves
or wings formed upon the projectile. Except for low veloci-
ties, all such experiments have failed to act with certainty,
and the end has been attained only by the positive means
mentioned in Chapter I.
XVI. — PROJECTILES.
Twist.
The inclination of a rifle groove at any point is determined
by the angle which its tangent at that point makes with the
axis of the bore. Twist, is the term generally employed to
express this inclination.
Classification of Twists.
When the inclination of the groove to the axis of the bore
is constant, the twist is called Mniform. When it increases
from the breech to the muzzle, the twist is increasing.
Figure 1 shows the development of the surface of a bore
rifled with uniform and increasing twists. Such curves are
traced for the construction of templets, by which a combined
motion of rotation and translation is given to the cutting tool
of the rifling machine.
Discussion.
Let q) be the inclination of the groove at any point; and
oa the angular velocity imparted to the projectile from being
constrained to follow in the groove while moving in the
direction of the axis with a velocity of translation v. Let r
be the radius of the projectile.
We may consider the velocity along the groove to be the
resultant of two component velocities at right angles to each
other; viz.: z; and f/ tan q). The latter imparts to a point
on the surface of the projectile a tangential velocity
r Go=^v tan cp. Hence,
V
CD =z tan cp • (2)
That is to say that when the twist is uniform, the angular
velocity increases only with the velocity of translation
throughout the bore. When the twist is increasing, the
angular velocity further increases from this cause; and other
things being equal, it increases as the caliber diminishes.
Since the muzzle velocity of a given projectile is fixed by
independent considerations, the angular velocity at the
10 XVT. — PROJECTILES.
muzzle is measured by the tangent of the angle made at that
point by the tangent to the groove and the axis.
If / be the time required to make one revolution, and n
be the length in calibers over which the projectile must pass
in order to make one revolution, we have from Eq. (2),
ODrt ^7tr 7t
tan ^ = -— - = --— = -. (3)
The twist is accordingly generally expressed in terms of n.
It has been found that for ordinary artillery projectiles,
about three calibers long, the requisite steadiness is given
by imparting to the surface of the .projectile a tangential
velocity of about 200 f. s. at the muzzle of the gun. Hence,
7t V
200 = r ci? = tan a>. F= - V .\ n—n — — . (4)
n 200 ^ '
The value of n at the muzzle of the piece has generally
been determined empirically as above indicated; a safe
margin being allowed, smce no objection to a moderate in-
crease in twist exists but that pertaining to a diminished
energy of translation, and to the increased stress upon the
piece.
Recent analysis has determined the minimum twist at the
muzzle for projectiles of varying proportions.
It appears from this analysis that n is constant for similarly
proportioned projectiles of the same material, whatever be
the caliber; that it increases as the radius of gyration about
the axis of revolution and the density of the projectile in-
crease, and as the radius of gyration about an equatorial
axis diminishes. Also, that the above value for the surface
velocity is only approximate, since for the same projectile
this may safely diminish as the initial velocity diminishes.
Tangential Pressure on the Rotating Device.
Since, for the same muzzle velocity of translation, the sta-
bility of a given projectile depends only on the angular
velocity which it has acquired at the muzzle; it appears that
XVI. — PROJECTILES. 11
SO far as this is concerned, it matters not whether the angular
velocity be acquired only through or, the acceleration of
translation, or through the combination of this cause with
the gradually increasing twist.
In the first case, the angular acceleration, will be greatest
at first, when the gun and the rotating device are under
their maximum strain, and will diminish as they become
relatively stronger; thus making a disadvantageous distri-
bution of the work of rotation, although the quantity of work
W
done will be constant and equal to -^ — /^/ w^
2g
k, is taken as about 0.8 r in the linear units used for V,
In order to make this stress, particularly that upon the
rotating device, constant throughout the bore, so as to avoid
either excess or deficiency in strength, the angular acceler-
ation must be made constant. Herein lies the value of the
increasing twist; since at the breech the diminished value
of q) will compensate for the increased value of a\ and con-
versely toward the muzzle.
The determination of the precise form of the developed
groove is difficult, both theoretically and practically, since
the constancy of a depends upon the properties of the
powder employed.
It was thought for some time that a groove, the twist of
which uniformly increased with the length of the bore, and
having as its development a parabola, would give the best
results.
Recent practice indicates the advantage of employing a
semi-cubic parabola, of the form x^—2py, which, in the
case illustrated in figure 2, passes from a value of n=50 at
the breech, to n=2D at the muzzle. Figure 2 shows how
variously may be distributed the tangential pressures. To
steady the projectile on leaving the bore, it has been thought
12 XVI. — PROJECTILES.
advisable to give to a short portion of the rifling neai the
muzzle a uniform twist.
MEANS OF ROTATION.
I. MUZZLE-LOADERS.
Classification.
The first rifled pieces were muzzle-loaders, and hence the
projectile was necessarily of smaller diameter than the bore.
Rotation was imparted to it in two general ways:
1. By making the rotating device fit the grooves before
firing, by providing the projectile with suitable ribs or
flanges.
2. By making the device fit the grooves after firing by
causing it to be expanded by the powder gases, after the
manner of the gas check. Chapter VII.
Operation.
For this special purpose, and in all cases to avoid abrad-
ing the grooves, the rotating device was made of a softer
metal than the rest of the projectile; or, if formed on the
body of the projectile, had given to it a large area of con-
tact so as to accomplish the same result.
Since the axis of such projectiles did not normally coin-
cide with that of the bore, they could be centered^ or made
concentric with the bore, only by chamfering the edge of
the groove giving rotation, or by some similar device, the
operation of which was uncertain.
Comparison.
Examples of the first class are shown in figures 3 and 4.
Those with studs were until recently generally employed in
Europe. The Whitworth projectile, the surface of which is
a twisted prism, is a type of this class. It was once distin-
guished, but is no longer employed in new constructions.
The principal advantage of this class is that the projectiles
are certain to take up the rifle motion.
XVI.— PR0JECTIL1E5. 13
They require special adjustment to the gun, both
in manufacture and in loading; the escape through the
windage erodes the bore; the stud holes weaken the projec-
tile, and their arrangement in tiers, or the use of flanges
renders it difficult to adapt these projectiles to the increas-
ing twist.
Examples of the second class are seen in figures 5, 6, 7.
Their advantages are their adaptation to any gun of the
proper caliber and the facility with which they can be load-
ed, particularly in action. The former advantage led to
their general employment during the Civil War, owing to
the elasticity of the conditions then prevailing. Only the
weight and the caliber of the projectile were fixed ; so that
inventors were free to adopt many ingenious variations of the
expanding principle. This is accordingly known as the
American system. It answered well the demands of the
situation but was uncertain in its operation; the expansion
sometimes failing and the entrance of the powder gases be-
tween the body of the projectile and the rotating device
serving sometimes to tear this from its seat. See figure 7.
The expanding cup has sometimes been applied to pro-
jectiles of the first class so as to prevent the escape of gas
above cited.
Examples of Class II.
The Butler and Eureka systems are the principal exam-
ples of the second class retained for the muzzle-loading
cannon still in service.
The Butler System. Figure 5.
The distinctive feature is the double lip formed in the
expanding ring. The outside lip is expanded into the
grooves, while the inner one is pressed against the tenon
on the base of the projectile with an intensity proportional
to that of the gaseous pressure.
14 XVI.— PROJECTILES.
The Eureka Projectile. Figure 6.
The base of the projectile is a frustum of a cone in which
the grooves, «, are cast. The expanding brass cup fits on
the frustum and is prevented from turning by correspond-
ing projections on its inner surface, and from falling off
during transportation by the screw plug, b.
On firing, the cup is forced forward and expanded into
the grooves.
II. BREECH-LOADERS.
In breech-loading cannon the chamber is of larger diam-
eter than the bore, and permits the use of a projectile pro-
vided with a compressible device.
Beside the advantages named in Chapter XI, the advan-
tages of this class are certainty of action, better centering
and the absence of windage. These qualities have caused
their general- adoption to follow that of the cannon in
which they are employed.
History.
Following the analogy of projectiles for small arms, it was
at first attempted to coat them with lead, cast over the body
of the projectile. But this was weak, the lead fouled the
bore, was easily deformed, and added useless weight to the
projectile when it was fired against armor. The length of
the bearing prevented the use of the increasing twist, and
the manner of applying the lead tended to alter the struc-
ture of projectiles of hardened steel. Such were the pro-
jectiles used by the Germans in the war of 1870.
To overcome these objections, narrow rings or bands of
copper, which is much stronger than lead, were placed in
pairs at equal distances from the centre of gravity. Their
diameter was equal to the caliber measured between the
bottom of the grooves, or slightly greater, while that of the
body was a little less than that between the lafids. Such
projectiles required the uniform twist.
XVI. — PROJECTILES. 16
To this class belongs a projectile used in the small
Hotchkiss cannon; figure 9. It has a thin sheet brass belt
about one caliber wide, compressed radially into a shallow
groove of equal width which is symmetrical with the center
of gravity. The surface of the groove is circumferentially
fluted, as seen in figure 9. When the piece is fired the
powder gases press the band into the flutings, forming a
series of rings, figure 10, which permit the metal to flow
backward as the band takes the rifling. These bands are
much cheaper to make and weaken the projectile less than
the solid rings formerly employed in these projectiles.
This ingenious method is confined to small calibers.
Present Practice.
The increasing twist now used in all large cannon re-
quires a narrow bearing, which, to diminish the effect of the
oblique action of the powder gases is situated in rear, at
such a distance from the base of the projectile as to give
sufficient shearing strength to that portion lying in rear of
the band.
To center the projectile a second band was formerly
placed in front, but this has been replaced by a very slight
enlargement of the body of the projectile near the base of
the head. Figure 21.
Position of the Eotating Band.
Although, for ease in loading, the difference of diameter
between the front bearing and the lands is made as small as
is safe; unless certain precautions are taken, the oblique
action of the powder gases — in a manner not thoroughly
understood — may set up a nutatory or oscillating motion
as the projectile travels through the bore. This leads to
inaccuracy, reduces penetration, and may even leave the
marks of the rifling on the front portion of the projectile.
To diminish this effect, the front and rear bearings should
be made the loci of conjugate axes of suspension and oscil-
16 XVI. — PROJECTILES.
lation. When the position of the front bearing is determined
by the shape of the projectile, this can be accompHshed by
swinging the projectile as a pendulum on a diameter of the
front bearing, and ascertaining the time, /, of one vibration.
Then the band should be placed at a distance from it,
I = g l—\ since f=7t\/ — {Michie^ Eq. 404.)
In order to diminish the effects of the oscillation in pro-
jectiles in which, from unavoidable differences in manufac-
ture, the method above described does not suffice, the width
of the rotating band should be made as great as the nature
of the twist permits. It is usually taken as about one-tenth
of the caliber.
LONGITUDINAL SECTION OF THE PROJECTILE
Profile.
The value of k in Eq. (1) depends largely upon the profile
of the meridian section of the projectile and the nature of
the surface. In the last respect breech-loading projectiles
of the last class have a decided advantage over those of the
first class of muzzle loading projectiles, since the atmocpheric
friction is much less. This has required revision of the
ballistic tables computed for the non-centered studded pro-
jectiles for which these computations were originally made.
The resistance of the air is not affected by the form of
the extreme point, which, even if flat, is supposed to carry
along with it a pointed core of compressed air; but the cur-
vature of the head of the projectile is of great importance
in that it affects the passage of the stream lines of air past
the shoulder^ as is called the circle of tangency between the
head and the cylindrical portion of the projectile. The cur-
vature of the head is expressed by the length of the radius
of curvature in calibers. This varies from 1.5 to 2.0 calibers.
XVI. PROJECTILES. 17
The form of the base is also of importance, in that, if also
curved, it facilitates the flowing of the compressed air into
the vacuum formed in rear of the projectile and so diminishes
the difference of pressure upon the two extremities of the
projectile ; to which difference the retardation is principally-
due. Examples of this may be seen in the Whit worth pro-
jectile and in the Hotchkiss projectile, already described.
This advantage is not generally utilized, as it tends to diminish
the sectional density, the strength of the base, and the facility
of manufacture and of stowage.
Mass.
The mass of the projectile should be distributed so as to
bring the center of air pressure as close as possible to the
center of mass so as to diminish the overturning moment of
the resistance of the air. This is a difficult matter, as the
direction of the pressure is constantly changing; it is there-
fore adjusted empirically by firing projectiles so weighted
that the position of the center of mass may be varied
INFLUENCE OF THE CALIBER.
Following the principle of similitude by which cannon of
the same class vary their linear dimensions in a given ratio
to their calibers, it appears: —
1. That the muzzle energy varies with the charge of
powder, or as the cube of the caliber.
2. That the capacity to convey this energy to a distance
varies as the first power of the caliber.
3. That the terminal energy varies as a power of the caliber
which increases from about 3 at the muzzle to about 4 at the
extreme range of the smaller of two pieces considered.
STRUCTURE AND MODE OF OPERATION.
Projectiles are classed according to their structure and
mode of operation as follows : —
18
XVI. — PROJECTILES.
1. Solid shot, or shot,
2. Shells.
3. Case shot.
T. SHOT.
Shot are used for penetration, generally of armor and in
small arms against animate objects. For cannon they are
confined almost wholly to the sea coast service. In order
to diminish the effects of internal strain due to differences
in the rate of cooling, shot are made not wholly solid but
with an empty concentric cavity or core, figure 11. In such
projectiles the point is carefully preserved.
II. SHELLS.
The increase in sectional density resultmg from making
spherical projectiles solid, having been attained by a change
of form, solid shot are now replaced by those which are
hollow and whioh can therefore convey energy in a form
unaffected by retardation.
Shells are hollow projectiles containing an explosive and
generally a fuze for its ignition at any desired point of the
trajectory, The fuze may operate at a distance which is a
function of the time of flight, when it is called a time fuze;
or the explosion may result more directly from the arrival
of the projectile at the point of impact. Such are called
impact fuzes. Each class of fuzes, as will be seen, has its
special province.
The size of the cavity depends upon the specific function
of the projectile. If this is intended to convey energy mainly
in the kinetdc form, the smaller the cavity, the greater is the
sectional density, and the more violent is the explosive
required. If the energy is to be mainly potential, the larger
the cavity the better the effect, provided that the resistance
of the projectile to the shock of discharge is not unduly
diminished.
XVI. — PROJECTILES. 19
The number ot pieces resulting from an explosion, and
the facility with which the bursting charge wili" operate, in-
crease with the brittleness of the material and with the
completeness with which conversion occurs before rupture
of the envelope occurs. Since for firing against troops frag-
ments below about one ounce in weight are not considered
dangerous, it is desirable to increase the number of fragments
of about this weight as much as possible and so to compensate
for the large, single mass formed by the base of the shell.
The sectional density of the fragments approaches con-
stancy and practically increases as they approach the spher-
ical or cubical form ; therefore, many devices have been
employed to regulate the rupture of such projectiles, as by
making the walls double, figure 12 ; by giving to the cavity
a polyhedral form ; or by grooving it spirally so as to dimin-
ish the tendency to burst in a meridian plane.
This appears from the following elementary analysis.
Tet R and r, be the exterior and interior radii of a shell,
the tenacity of which is T, supposed uniform throughout the
section. Then, for the meridian rupture of a unit of length
the necessary pressure will result from the equation —
2r/ = 2(i?-r)r.-./=r('^-lY
for an equatorial or transverse rupture we have
Operation.
The rupture of a shell will occur in one of the two ways
above indicated only when the material is thin and inelastic, as
in some shrapnel to be described. When, as is usually the
case, the projectile has thick walls (Chap. V), the inner con-
centric layers are more extended than those outside,they are fis-
sured until fracture is determined by the line of least resistance,
20 XVI.'— PROJECTILES.
and the fragments are scattered by the energy remaining in
the gases. The resistance of the envelope should therefore
be kept within certain Hmits.
Shells used against armor are pointed, and are filled and
fuzed from the rear. They replace shot whenever possible
since their penetration can be made almost as great, and
their effects after penetrating the sides of a vessel are much
more destructive both to men and machinery.
Against masonry, shell serve a double purpose; first to
penetrate the wall and fissure it by their explosion; and
second, by throwing out the fragments to present a fresh
surface for the next blow.
Shells used against earthworks should contain the largest
possible bursting charges. Such are called torpedo shells.
They are sometimes made 6, and even 8 calibers long and,
owing to the vertical angle at which they strike, are fired with
low velocities from mortars and howitzers.
A grenade is a form of shell, generally spherical, intended
to be thrown by hand or to be rolled down a parapet against
masses of troops making an assault.
BURSTING CHARGES.
Gnnpowder.
When powder is used it is preferably of fine grain and of
high gravimetric density. Such powder in firing, has a
tendency to cake^ or become compressed into a mass of such
density that the removal can be accomplished only by the
chisel. This increases with the length of the charge and
evidently tends to defeat its object.
The caking, as indicated by the letters a, b, c, in figure 13,
results from three causes; viz.: a, from the shock of dis-
charge; b, from the rotation of the projectile, and <r, from
the shock of impact.
XVI.— PROJECTILES. 21
The effect is to compress the powder and diminish its
inflammability. If the impact be sufficiently resisted, the
solidified mass may be thrown forward with such energy as
to cause its ignition. To diminish caking, the cavity is
often varnished; and to delay the explosion of armor piercing
shell, the bursting charge is sometimes enveloped in flannel.
On the other hand, where promptness is required, the French
place loosely in the cavity a small wooden prism, figure 14,
containing on two of its sides a network of oblique grooves
through which the gases resulting from ignition may pene-
trate the indurated mass. A slip of wood is tied over each
grooved surface to prevent the channels from becoming
choked.
The bursting charge has been advantageously made of
discs of concrete powder, strong enough to resist the causes
leading to a and b, figure 13, but disintegrating under the
influence of ignition. Such charges require to be filled
through a hole, the size of which is objectionable.
High Explosives.
Gun-cotton is not injured by caking and, when specially
prepared, does not readily explode on impact. This, or some
equivalent high explosive, appears to be required for shells
in which the excessive fragmentation of the envelope is not
objectionable. This objection may be removed by using
a small charge of dry gun-cotton in a shell filled with water.
A high explosive is particularly required in armor piercing
shells; these, if strong enough to penetrate the armor, may
fail to burst with the utmost powder charge whrch they will
contain or they may explode harmlessly before penetration
is complete.
The comparative insensibility of explosives of the Bellite
class would seem to fit them particularly to this purpose;
although the gx&dX force of gun-cotton makes it well adapted
for use against earthworks. Its explosion is said to reduce
22 XVI. — PROJECTILES.
a large spherical zone of earth to a pulverulent form, by
which its removal, and the exposure of the masonry which
it is intended to protect, are facilitated.
Sizft of Cavity.
Great advantage has been found to result from increasing
the size of the cavity by making the envelope of the shell
of thin steel tubing. A 12 pound shell so made was found
more effective against earthworks than a 50 pound shell of
cast iron. To produce their full effect, such projectiles
require an independent steel base, concave on its interior
surface, so that it may be expanded against the walls instead
of being driven outward by the explosion before the powder
is entirely converted into gas.
INCENDIARY PROJECTILES,
Although the explosion of the bursting charge may suffice
to ignite the splintered fragments of wooden structures,
greater certainty in the effect results from filling the shell
with an incendiary composition ignited by the discharge
and flaming through specially constructed apertures in its
walls. Such projectiles, called carcasses, and also red-hot
shot, were formerly employed against wooden vessels.
To this class may be referred light balls, thrown at short
ranges to burn on the ground and illuminate the works of
an enemy during a siege. To prevent their extincti*on, they
were made to contain a loaded shell or a number of loaded
pistol barrels.
A more recent form consists of a shell containing a para-
chute which is distended when the shell explodes, and,
when carried over the enemy's works by the wind, illumi-
nates them by the light of a mass of incendiary composition
suspended beneath it.
For modern warfare such devices are superseded by the
XVI. PROJECTILES. 23
electric light, projected from under cover by a reflecting
surface.
III. CASE SHOT.
Where concentration of energy upon a given point, and,
therefore, accuracy is required, shell, or preferably solid
shot are used; but where, owing to the dispersion of the ob-
jects and their inferior resistance the energy should be
distributed, as in fowling pieces, case shot are employed.
Case shot consist of a number of small projectiles, which
we may call the cluster, contained in an envelope; according
to the method of their liberation from which they are divided
into two classes.
1. Canister and grape shot, which separate at the muzzle
of the piece in consequence of the shock of discharge. The
general name, case, is now usually reserved for this variety.
2. Shrapnel, which separate at a distance in consequence
of the explosion of a small bursting charge, contained with-
in the envelope.
These projectiles forcibly illustrate the principle of sec-
tional density in regard to the behavior of the projectile as
a whole, and to the operation of the component parts, includ-
ing the fragments of the envelope.
Operation.
The fragments separate in what is called the sheaf, or cone
of dispersion, of which the mean trajectory constitutes the axis.
Figure 15 shows a shrapnel provided with a time fuze, burst-
ing in air; and figure 16 one with an impact fuze, bursting,
as it is called, "on graze."
The right section of this cone is circular and the horizontal
section elliptical. The size and form of the ellipse for any
section vary with the energies of the different component
parts, horizontally in the plane of the trajectory and normally
to that plane; and also with the sectional density of these
parts.
24: XVI. PROJECTILES.
The inevitable lateral dispersion being sufficient for the
necessary distribution, it is sought by various means to
increase, at the moment of their separation, the component
energy of the parts in the direction of the tangent to the
trajectory. It is to the success of such efforts that the
superiority of shrapnel over case shot of Class I is due.
Case shot are generally employed against animate objects,
a dangerous wound to which is taken to correspond to
the energy required to pierce a pine board one inch thick.
It is convenient to remember that this requires a velocity
of about 500 f. s. in an ounce ball, or to an energy of about
one eighth of a foot-ton. A velocity of 500 f. s. is accordingly
taken as the limiting velocity for case shot.
For reasons given, the fragments of the envelope are in-
effective as compared with the members of the cluster, which
are generally spherical. The envelope is therefore made as
light as possible.
Structure.
But for the shock of firing, which deforms the members of
the cluster even to the extent of consolidation, and which may
even burst the envelope from the dilatation of its contents, the
cluster would always be made of lead. But lead is expensive,
and requires to be alloyed with tin or antimony; or to be im-
bedded in a matrix as of sulphur or rosin; or to be packe'd
in coal dust to resist this shock. Consequently, iron is used,
except when the conditions require every structural advan-
tage to be improved.
Iron has the further advantage in certain cases of making
the mean density of the case shot equal to that of the shell;
this permits the firing to be regulated as stated page 4.
The size of the balls depends upon the facility with which
the envelope may be filled, upon the material of which they
are made, and upon the distance at which, after separation,
they are required to act.
XVI. — PROJECTILES. - 25
CLASS I. CANISTER AND GRAPE SHOT.
These are distinguished by the lightness of the envelope,
which is designed only for their transportation and loading.
The balls, generally of cast iron, are now much smaller
than before shrapnel attained its present importance.
Canister.
For smooth-bore cannon the envelope consisted of a tin
case supported in rear by a disc which was designed to
prevent the penetration of the gases into the cluster v^hile
within the bore. To avoid the rotation of the projectile
in rifled cannon, the envelope is stiffened so as to prevent
its upsetting or dilatation into the rifling. In the English
service this is done by inserting three trough-shaped pieces
of sheet iron around the cluster. In the United States service
a thin tube of malleable cast iron, closed at one end, is em-
ployed. This is known as Sawyer's patent. The fragment-
ation of this tube is assisted by spiral cuts. See figure 17.
Since canister is retained only for the extreme simplicity
of its operation at the short ranges at which it is employed
by the defence, the size of the balls has been greatly
diminished.
When, as in the defence of the ditches of permanent works,
the desired eflect is not complicated by requiring projectiles
of different natures to be fired from the same gun, canister
fire is replaced by that from machine guns. This is continu-
ous and does not derange the aim so much.
Grape Shot.
These were formerly employed in smooth-bore guns
against both animate objects and the masts and rigging of
vessels. The iron balls were arranged in tiers of three,
sustained by a central spindle, a top and bottom plate and
two intermediate rings. Figure 18. In former times they
were quilted into canvas bags, whence the name.
26 XVI. — PROJECTILES.
CLASS II. SHRAPNEL.
Principles of Shrapnel.
Notation.
Let V be the initial velocity and v be the remaining ve-
locity of the shrapnel at its explosion.
Let Vy and v^^ estimated respectively at right angles to, and
parallel to the tangent to the trajectory, be the mean veloci-
ties of dispersion and of translation of the N balls that form
the sheaf, irrespective of the velocities in these directions
that are due to the remaining velocity v.
The velocity v^^ which is taken without regard to its sign,
may be due to either or both of two component velocities ;
viz. : 1st. The velocity v^^^ due only to the bursting charge;
and, 2d. In oblong projectiles, the velocity v^^^ due only to
their rotation.
The velocity v^ , which is an increment of the remaining
velocity, is due only to the bursting charge, and its sign de-
pends upon the position of the bursting charge within the
projectile.
Tet v' be the resultant velocity of translation due to z^± v^,
Tet qp be the inclination to the surface of the ground of
the tangent to the trajectory (the axis of the cone) at the
point of explosion. It is important to remember that, as
stated in Chapter I and to be proved in Chapter XX, the
curvature of the trajectory, or the value of qp measured from
the horizon, is a decreasing function of v.
Let Q be the angle at the vertex of the cone of dispersion,
figure 24.
We will for simplicity suppose the cone to be composed of
rectilinear elements, and the surface of the ground to be
horizontal,* so that d will be the angle included between
* For the effect of varying the inclination of the ground, see Chapter
XXX, figure 34.
XVI. — PROJECTILES. 27
the upper and lower tangents to the sheaf at its vertex,
figure 25.
Distribution, t
It is evident that the mean density of the sheaf will be a
decreasing function of ^=2 tan-^ —L Also, from the horizon-
tal projection in figure 24, that since — balls will be
found in the area a b o d, the smaller is ^, or the more nearly
does the cone approach a cylinder, the more uniformly will
the balls be distributed over the entire ellipse a b o d.
Also, the smaller the angle g), the greater is the eccen-
tricity of the ellipse ; or, for a given lateral dispersion, the
greater will be the dangerous space in the line of fire.
N
If a be the area of the ellipse, d= — will be the measure
a
of the density of the section ; this varies along the ellipse ; see
figure 24.
The shrapnel will be most effective when _ = — is the
mean area occupied by one man projected on the ground
by the elements of the cone.
Besides ^, g) and N the value of a will depend on the
height above the ground, and the distance in front of the
target at which explosion occurs, or upon the distance vo=h,
t Note. The curvature of the axis of the sheaf causes the section to be
not truly elliptical, but oval as in figure 25. The ascent of the balls in
the upper half of the sheaf, and the curvature of their trajectories due to
their small sectional density, reduces their striking energy, so that those
that fall near the large end of the oval are comparatively ineffective.
This loss will be partly compensated for by the ricochet of balls nearer
to the axis, provided they strike ground that is sufficiently hard. For
ricochet, the angle of incidence shonld be less than 20° : this establishes
a limiting value for g} -f" o <C^^°.
These differences between the actual and the assumed conditions, hav-
ing been understood, may, for this discussion, be neglected.
28 XVI. — PROJECTILES.
Nature of Target.
The requisites of shrapnel vary somewhat with the dis-
position of the troops against which it is to be used. These
may be:
I. Either in columns of manoeuvre, or in deep masses
which it is the object of the artillery to force to deploy at
long distances. In open ground these distances may uow be
as great as two miles.
II. Deployed in line at shorter ranges.
In the first case, consistently with the limiting values of
^j the values of 6 and /i should be small ; and conversely in
the second case. In the first case, as the enemy will gene-
rally be in motion, and therefore erect, cp also should be small ;
and in the second case, as the enemy will generally be lying
down and seeking cover, cp also should be large.
These conflicting considerations require special treatment.
In the first case guns with high velocities are needed, and in
the second case the limit will probably be found in the use of
field mortars. Between these limits guns may be used with
reduced charges and at high elevations, and at the closest
ranges, say within 300 yards, canister is most effective.
The two cases correspond to the limiting cases of the cone.
First, when = g) r= 0. Second, when 6 :=z cp =z 90"".
The first case, being that most comprehensive and difficult
to satisfy, and since it involves by its opposites the second
case, is that herein discussed.
Choice of Fuze.
Shrapnel may be exploded in the two ways shown in fig-
ure 16, viz., " on graze " by an automatic impact fuze, or in
the air by an adjustable time fuze. These have different
spheres of action as follows :
Impact fuzes may be used at short ranges where v is large
XVI. — PROJECTILES. 29
and and cp are therefore small; and where q' the angle of
reflexion (always greater than 9), is also small. Figure 16.
But they act irregularly when the ground is soft or rolling ;
and at long ranges when v is small and 9 is large, the energy
lost on impact reduces the already diminished value of v,
and consequently increases the value of 6, The time fuze
is therefore essential for soft or rolling ground, and for long
ranges over any ground. A possible objection to it applies
to the risk attending its premature discharge when firing over
friendly troops.
On some accounts the time fuze is less well adapted for use
at short ranges than is the impact fuze ; since for a given
error in the time of its burning,* the greater is z', the greater
will be the resulting variation in h, and therefore, for given
values of 6 and qp, the greater will be the variation in a.
Although this objection is partly neutralized by the small
values of 6 and (jp at short ranges, the conditions seem to re-
quire the use of two fuzes in each projectile. See the co7n-
bination fiize^ Chapter XVIII. Meanwhile the improvement
of the time fuze is one of the most important problems in
ordnance.
Computing the Value of d for Rifled Shrapnel.
Let p be the mean radial distance of the balls.
This is taken instead of the radial distance of the outer
ball, as is generally done, since the distribution of the balls
throughout the cross section of the sheaf is more important
than their extreme lateral dispersion.
Let r be the external radius of the shrapnel, taken equal
to that of the bore of the gun.
Although Fwil be reduced during flight, it is assumed,
and experiment confirms the assumption, that at ordinary
* The mean error (Chapter XXX, page 24) in the time of burning may
be taken as about 0.05 sec.
80 XVI. — PROJECTILES.
ranges the angular velocity of the projectile does not sensibly
diminish.*
Under this assumption, from Equations (2) and (3) the tan-
gential velocity of the mean ball will be nearly
P" = ;~^. (5)
and, since we are considering only the tangential velocity due
to rotation, we have Vjy = p cj and
6 p 0) pn F . -.
tan - = '-J- = "^ ,. (6)
If we substitute in this equation the empirical value of n in
Equation (4) we have,
tan-=-y--^, (7)
and for a given shrapnel in which V^ n, and - are known,
tan|=|; (8)
an equation easily remembered, and which agrees fairly well
with practice.
History.
The history of the improvement of shrapnel, which is now
the principal field artillery projectile, illustrates many impor-
tant principles. As stated, page 24, improvements liave
tended to reduce the ratio -~- , and to increase the sectional
7/
density of the projectile as a whole, and that of the balls it
contains.
Spherical Shrapnel,
I. Shrapnel, as invented in 1808, by General Shrapnel of
the British service, were simply spherical shell, loaded loosely
with musket balls and a bursting charge.
* Projectiles fired vertically upward have returned to the earth with
sufiicient rotation to keep them point foremost.
XVt. — PROJECTILES. SI
In transportation the powder was triturated by the balls,
and on firing the piece the shock might cause a premature
explosion, or might conglomerate the balls ; sometimes even
.causing the projectile to be ruptured by the resulting dilation
of the cluster. The ignition of the bursting charge at the
proper time was also uncertain.
In order to make F large enough to give a large value to
Z', the walls of the shell were made thick enough to stand a
heavy propelling charge. But this diminished the value of
N^ and, since the interstitial volume between the balls was
large, 7u had to be made large in order to obtain sufficient
pressure to burst the shell. The energy remaining in the
powder gases after rupture of the walls being large, the balls
were widely scattered, making 7>y large. The resultant value
of vx was zero. At long ranges, tan - = -^ was there-
fore large.
2. The next step was the invention of spherical case, much
used during our civil war.
By imbedding the balls in melted sulphur and boring out a
chamber for the bursting charge, figure 19, the value of iv
could be decreased, and the certainty of its ignition at the
proper time be increased. The matrix supported the walls in
firing, so that their thickness could be decreased and N be
increased. But the matrix often retained the balls after ex-
plosion, and the value of 7^x was still zero.
3. Colonel Boxer, of the Enghsh army, devised a shrap-
nel, figure 20, in which the balls, hardened by an alloy of
antimony, and packed in coal dust, were separated from the
bursting charge by a wrought iron diaphragm around which
the envelope was cast. The seat of the diaphragm and sev-
eral other meridional grooves served to weaken the envelope
and to diminish the value of w.
While the projectile was necessarily fired with the fuze in
32 XVI. — PROJECTILES.
front, the non-coincidence of the centers of figure and of
mass caused the resistance of the air to turn the Hghter
portion of the projectile to the rear, so that z^x was always
positive.
This projectile marked the farthest advance of spherical
shrapnel.
Oblong Shrapnel.
The advantages of the oblong form of shrapnel are as
follows :
It permits the base of the envelope to be strengthened
without increasing the thickness of the walls. This, with im-
provements in cannon and gunpowder, has increased the
value of Vj and since the sectional density has been increased
so that at long ranges ^ has been diminished, it has also in-
creased the eccentricity of the section of the cone of disper-
sion by the ground. By placing the bursting charge in rear,
Z'x has become positive, and z'yb has become practically zero.
An example of such a projectile is seen in figure 21, in
which B^ is the cast iron body ; H, the ogival head of wood,
covered with a sheet iron cap by which it is riveted to B ;
C, the powder chamber, made conical to facilitate unloading;
Z>, a disc by which the cluster is swept out to the front; T, a
tube to carry the flame from the fuze, 7% to C. A paper lining
keeps the rosin matrix from adhering to the walls of the cavity.
The shght resistance of the attachments of the head makes
of this projectile a sort of aerial gun.
The objections to this projectile indicate the nature of re-
cent improvements. The wooden head, the tube, the disc,
and the thickness of the walls required by the nature of cast
iron, diminish JV so much, that the balls form about one-
quarter the weight of the whole projectile.
The bursting charge is too small to produce sufficient
smoke to indicate the explosion at distant ranges, and thereby
to assist in correcting the aim.
XVI. PROJECTILES.
The position of the bursting charge is such that, while
acting well in air, when used with an impact fuze the delay-
caused by the passage of the flame through the tube causes
the projectile to rise too high before bursting.
Present Practice.
The most recent ideas on the subject are embodied in
figures 22, 23.
Figure 22 contains a combined time and impact fuze.
The bursting charge is situated in front, occupying the
room which in figure 21 is wasted. It is large enough to
give the smallest volume of smoke visible at extreme ranges.
The envelope consists of a thin drawn steel tube, secured
in rear to a separate base, and slit and compressed in front to
an ogival form.
The cluster consists of a column of leaden balls, separated
by discs of cast iron. The discs are sunken to fit the balls,
and form a skeleton matrix.
When the bursting charge explodes, the slit ends of the
point are thrown back, so as to dirhinish the sectional density
of the envelope as compared with that of the cluster.
The latter moves on with v' z=.v — v^ =v — about 200/. s.
Figure 23 represents a more recent form, of which in 1891
a number are in process of manufacture for experimental trial.
Its construction is apparent. The tube is of thin brass,
enlarging its capacity for powder, and facilitating the passage
of the flame from the fuze. The w^alls are weakened by
longitudinal grooves. It remains to be seen whether, com-
pared with figure 22, the increase in 7'yb resulting from this
construction will not neutralize the increase in Vyr^ ,
THE SEGMENT SHELL.
An attempt was made some years ago to combine the
functions of solid shot, shell and shrapnell in the segment
shell, in which the cluster was composed of the sectors of
S4 XVI. — PROJECTILES.
concentric cylinders arranged so as to form a solid mass.
But such a violation of the principle of the independe^ice of
function^ which requires that where simplicity permits, eacli
specific function be separately provided for, necessarily
failed. The importance of this principle in the design of
machines of all kinds can hardly be too forcibly stated. The
opposite of this idea, that of combination, by which more
than one office or function is expected of any one member
of the machine or organization, is seldom found to be com-
patible with the efficiency of the whole, as we shall have
many opportunities of seeing during this course. The full
development of the principle of the independence of function
leads naturally to complication or the multiplication of parts;
judgment is therefore required to compromise between sim-
plicity and efficiency. The history of invention appears to
indicate the pre-eminence of efficiency.
As a case in point, it is now conceded that three types of
the two classes of projectiles are required for field and siege
artillery; viz.: shell, to convey kinetic energy for penetration,
and potential energy for demolition and moral effect; and
case shot for kinetic energy only. Although shrapnel, when
reversed in the gun, may in an emergency replace canister;
it is better to carry a few rounds of the latter, preferably,
as in the British service, on the carriage which supports the
piece.
REGULATING SHRAPNEL FIRE.
Referring to figure 24 we may consider the horizontal and
vertical projections of //, viz., x — h cos cp ; j^ = A sin gi.
Of these quantities, which are separately discussed in the
regulation of fire, x is mainly varied by changing the time of
burning ; and y by changing the angle of fire.
Under given conditions x varies inversely as the range.
Its variations, however, are not great, since there are com-
pensations that tend to keep it constant. It is found that
XVI. PROJECTILES. 35
the best results follow a value of j\; = 50 yards for all dis-
tances except those very short, for which x may increase up
to 100 yards. If x be taken too small, too great a propor-
tion of the shrapnel fired will explode beyond the target and
be wholly lost.
In order to utilize the small values of qp in the upper half
of the sheaf, it is advisable to make y small. It is found
that the best results follow a value of y varying from 2 yards
at 500 yards range, to 6 yards at 2,500 yards range. Greater
values of y are not used, since they are difficult to observe
correctly at long distances. The reason for the increase of ji^
is due to the increase of cp at long ranges, and the consequent
decrease in the area of the section cut from the cone by the
surface of the ground.
These rules are in the nature of approximations. In prac-
tice the fire is regulated by signals from observers, placed as
far as possible to the front and flank.
EMPLOYMENT OF FIELD PROJECTILES.
Shells.
These projectiles when used with a time fuze would follow
the principles laid down for shrapnel ; but the large value of
6 and the small value of N would make this unprofitable.
They accordingly use an impact fuze, which makes of them
the best means of controlling elevations. See page 4, and
Chapter XXX, page 20.
They are generally used against inanimate objects to be
demolished, pierced or set on fire.
In the following cases they may be used against troops :
1. At distances too great for the time fuze.
2. When the enemy is hidden in a village, or in thick
woods.
The violence of their explosion assists their moral effect,
particularly against horses and fugitive masses.
36 XVI. PROJECTILES.
Shrapnel.
These are exclusively used against animate objects in the
open, or in thin cover. They were found very destructive in
the Russo-Turkish war. In siege oper ttions they serve to
annoy parties working at night to repair the damages done
by day.
PENETRATION OF ARMOR.
General Considerations.
The penetration of armor depends principally —
I. Upon the nature of the armor. In the order of resist-
ance armor may be classed as follows :
Cast iron with a chilled face, used only for land defenses
and not considered herein.
Steely forged and tempered.
Compound^ viz., a wrought-iron back with a hard steel
face.
Wrought iron^ now obsolete.
Roughly speaking, armor yields either by ptinching or
racking. In the first case, as in wrought iron, the effect is
local. In the second case, the energy of impact is distrib-
uted throughout a greater mass of the plate and tends to
crack the plate or to wrench it from its fastenings. The effect
is mainly to remove an obstacle to further penetration. Cast
iron armor yields in this way, and so do steel armor and the
face of compound armor if too brittle.
The object of the artillerist is to concentrate energy on a
small area, so as to reach the objects which the armor is in-
tended to protect, /. e., to punch.
The object of ihe armor-maker is to protect these objects,
by distributing the energy of impact as much as possible
between the projectile and the mass of the plate, so that even
at the risk of destroying the plate by racking, the shot must be
kept out.
XVI. — Projectiles. 87
But if racking can be avoided without loss of resistance to
punching, the quahty of the plate is improved. In the early-
manufacture of armor, racking effects predominated ; these
disappeared as its manufacture was improved ; while the resist-
ance to punching was maintained or even increased. For ex-
ample, the principal objection to steel, for armor as for other
purposes, has been its brittleness. But at Annapolis, in 1890,
carbon steel armor resisted punching, but was slightly racked.
Nickel steel armor resisted both racking and punching. Com-
pound armor failed in both respects.
The nature of the backing or support against which the
plate rests, considerably affects its resistance. Except for
compound armor, for which the backing cannot be too rigid,
the backing should be somewhat elastic, so as to absorb
energy, after the manner of a cushion supporting a board in
which one seeks to drive a nail.
As the liability to racking increases, the number of the
bolts by which the armor is held in place should also increase,
so as to retain those portions which would otherwise be
displaced.
II. As a consequence of the above must be considered
the resistance of the projectile to permanent deformation ;
page 3.
III. Upon the striking energy of the projectile, measured
in a direction normal to the plate.
Since the projectile acts after the manner of a punch,
shearing its way through the plate, the energy is often
estimated per unit of circumference. In earth and masonry,
in which the material is soft, the projectile is supposed to
compress it to the front, and the energy is taken per unit of
area of cross section.^
* As experience with plates and projectiles of varying resistance to per-
manent deformation, increases, such assumptions are gradually replaced
by purel) empirical formulae suited to each special case.
J^8 XVI.— PROJECTILES.
Whereas in experimental tests normal impact is the rule, in
firing at ships it will be the exception. The shape of the
point of the projectile also tends to make it glance, so that
for these reasons armored ships may be expected to resist
more than the formulae predict.
Haitian d's Formula of 1880.*
The energy expended in other forms than in perforation,
as in heating the plate and projectile, and in deforming the
latter, has given rise to many empirical formulae, some of which
may be found in the Course of Permanent Fortification. A
very successful formula, Froloff''s^ assumes that -the energy so
lost is proportional to the striking velocity, so that the pene-
tration is proportional to the momentum of the projectile on
impact. The following formula, which illustrates a principle
already taught, is considered by recent writers to be one of
the best Equation (15).
Let t be the thickness in inches, of wrought iron armor that
would just be perforated by a cast iron projectile, whose
weight is W^ its normal velocity on impact v^ and its diam-
eter d.
Let e be the normal energy in foot-tons, or ^ = tt— s?r<7r
^^ 2^^ 2240 .
Let s be the energy in foot-tons per inch of circum-
ference, or f = =- .
TT a
During a prolonged series of experiments made by Colonel
Maitland it was found —
1st. That / varied directly with £, or
'=/(■?)■ «
* It is inferred that the experiments on which Maitland's formula is
based were made with ordinary cast iron projectiles, and that the armor
was backed.
XVI— I^ROJECTILES. 80
2nd. It was also observed that when projectiles of different
calibers were arranged in classes according to their spherical
densities; in each class the penetration measured in calibers
was very nearly proportional to the striking velocity.
For a particular class, known as the standard projectiles, of
which the spherical density was 3.0, the penetration was nearly
one caliber for every thousand feet of striking velocity. This
is known as Captain Orde-Browns *' rule of thumb."
For purposes of comparison, let us assume a given gun to
be fired against a given plate ; d and / will then be constant,
and the variation in spherical density will result from varying
the weight of the projectile. The variables will then be W
and V. For the standard projectiles let these be represented
by W, and v^,
Owing to the number of experiments made with the stand-
ard projectiles, special weight is given to the results obtained
from them. These results are expressed in the following
general formula, differing slightly from Orde-Brown's rule,
viz. : « = ISOO - *^-^^- (^">
To pass from standard projectiles to those not standard,
we use Equation (9) in order to ascertain the relation between
V, and V, Under the hypothesis that d and / are constant it
becomes v ^ f y\j ^ ' (11)
Whence v\v\\ Jw : y/W„ or z; = v \/^. (12)
In the standard projectiles, J^= 0.375 ^/^ ; whence, from
Equation (11) ,, = 1^^^^W^ (13)
Substituting in Equation (10) we have
40 XVI. — PROJECTILES.
Y/f__0.14; (14)
"- 612.4 d
Whence, multiplying both members by d^
'="'^= ski \/f-- 0.14^. (15)
The value, /, thus obtained is the thickness of a plate that
will just be perforated by a projectile having an ogival head
with a radius of curvature of 1.5 calibers. If the radius of
curvature is increased to 2 calibers, as is now customary, t
will be increased by 5 or 10 per cent, and Orde-Brovvn's rule
will increase in exactitude.
If the plate resists perforation, then the penetration may
be taken as about 0.9 of the estimated perforation.
The Formulae of De Marre.
The following formulae result from recent experiments in
France and, except for Equation (20), cover a great range in
calibers, and in the ratio - .
d
In the English units previously used we have for modern
projectiles, viz., chilled iron shot and steel shells.
I. For the perforation of wooden backing when used as
such, i. e., not unprotected
^b = 0.1823 / ^-^ ^ ••« (16)
This is about 70 per cent greater than when the backing is
unprotected.
II. For a wrought iron armor plate that is hacked ; the
resistance of the plate alone being considered
^j = 5.809 /^-V-^ (17)
Owing to the improvement of projectiles since 1880 this
is less than the value implied by Equation (15).
XVI. — PROJECTILES. 41
For the entire target consisting ot the plate and backing
^i = ^i + ^b. a8)
III. For the rather soft steel plates^ generally used for heavy-
armor, as made at Creusot, when backed
^3 = 7.286 Z'-*^'-"* (19)
See also Equation (18).
IV. For the thin plates of hard steel, unbacked, used for gun
shields, when attacked by the comparatively small cannon
known as Rapid- Fire guns and Revolving Cannon
^p = 12.86 /'-^^'-^ (20)
These formulae, while abundantly verified in the French
service, must be accepted with caution when the conditions
differ from those under which they were deduced.
Very's Formula.
Mr. E. W. Very, formerly of the U. S. Navy, has recently
proposed a means of comparing the resistance of steel plates
that has long been desired, since it eliminates variables
relating to the nature of the plate, its thickness and the cali-
ber and velocity of the projectile, all of which may differ in
experiments made at different times and places.
It assumes that the projectile is not deformed, and that no
other effect is produced but that of punching, which is sup-
posed to be complete. The effect is referred to that pro-
duced in wrought iron, since withm ordinary limits all such
armor is homogeneous, and is therefore, well adapted for use
as a standard of comparison.
Suppose we find by trial that a certain projectile will just
perforate a given steel or compound plate with a certain
energy e^. Calculate the energy e^ required for the same pro-
jectile to perforate a wrought iron plate of the same thickness,
e
and similarly backed. Then -1 z= g), m which qp is a factor
42 XVI. — PROJECTILES.
expressing the relative per cent of energy required to per-
2140
forate the steel plate, e, g. ^-— — 107 per cent.
Since 1880 the improvement in projectiles has been so
great that e^ has decreased considerably. Improvements in
the quality of steel armor have increased e^, so that (p has in-
creased from about 125 to over 150. See next topic.
Weaver's Formula.
It has long been thought that besides its thickness, the mass
of the plate affects its resistance to penetration, and conse-
quently the '■^ energy per ton of plate^'' is often recorded in the
reports of firing against armor. No use is known to have
been made of this knowledge, however, until the following
formula, proposed by Lieut. Weaver of the U. S. Artillery.
• It is probable that the work is practically confined to a
mass of some definite volume immediately surrounding the
point of impact, and that the volume of this mass is a cylin-
der, the diameter of which is n times the diameter, d^ of the
projectile, and the height of which is /, the thickness of the
plate.
Experiments show that a notable increase in temperature
and the bulge are confined to a tolerably distinct ring, about
2 calibers wide, so that n is probably not less than 5. It is
probable also that it is safe to allow for an exterior ring which
absorbs part of the energy, although the effects in this ring
are not apparent. The value of 7i also depends upon the
relation between t, the thickness of the plate, and d, the
diameter of the projectile. Lieut. Weaver expresses this re-
lation for Creusot steel by
n = 6.25 + 0.22 (/ — d) (21)
in which / and d are in inches. This value will depend upon
the rigidity of the material, and is subject to correction by
experiment.
XVI. PROJECTILES. 43
In wrought iron n will approach unity, as the effect is
noticeably local and no great increase of temperature in the
adjacent parts is observed.
From a general consideration of records Lieutenant Weaver
finds that about 1828 foot tons of energy per ton of plate is
necessary to perforate the entire target, consisting of a steel
armor plate and its backing. This assumes the plates to be
substantially uniform in resistance, the projectile to be inde-
formable, and neglects secondary effects, such as racking.
Calling this coefficient, C ; the weiglit in tons of the disc in
question, W^\ and the weight in tons of one cubic inch of
the plate, w; he writes :
£.= ff/,C=(«-'^)%/.^C (22)
Supposing w — log ~^ 4.1028 and substituting for tt, w and
C their values, we have the general formula
A = 0.1828 ie d^ t (23)
APPLICATION.
We may now compare the foregoing formulae by reference
to the experiments at Annapolis in September, 1890. The
plates were 10.5 inches thick, backed by 36 inches of oak,
and were fired at by steel shells, as follows :
No. of fT- ■■ , TT^ Spher. Effect on
shots. ^^^"^- '^ ^^ Dens. ^ ' Projectiles.
8 Holtzer Steel, 6 in. 100 lbs. 3.70 2075 2988 6 unbroken.
2 Firminy " 8 " 210 " 3.28 1850 4988 2 broken.
Confining our attention to the unbroken 6 inch projectiles,
only the points of which perforated the carbon and nickel
steel plates, Lieutenant Weaver's formula gives ^g = 362 L
If from this we subtract e^ = 77, per Equation (16), we have
e^ = 3544, which is 18 per cent more energy than the plates
received from any one blow. As the plates were not com ■
plete^ perforated, this would indicate that the value of
44 XVI. — PROJECTILES.
(p z= 195 from Equations (18, 21) is more nearly correct than
that of (p = 158 assigned by Mr. Very's method ; viz., by
dividing 2988 X 100 by the vaUie of c, = 1816, given by
Equation (18).
ROCKETS.
Definition.
A rocket is a projectile propelled by a source of energy
which it contains ; it therefore performs also the functions of
a cannon.
Structure.
A rocket consists of a cylindrical case of paper or metal,
containing a composition formed of the ingredients of gun-
powder mixed in suitable proportions. The front end of the
case is usually closed, but the other end contains one or more
holes or vents for the escape of gas from the ignited compo-
sition. Within the rocket is a hollow space called the bore ;
this may be formed by driving the composition around a
spindle which is afterwards withdrawn ; or by boring out the
composition after its compression to a solid state.
The case is surmounted by a pointed head, which, for
signal rockets, consists of a hollow paper cone, and for mil-
itary rockets of any suitable projectile Depending upon
the particular system of construction, some means is also
provided for guiding the rocket in its flight.
Composition.
Since the composition is required to ignite readily, and
since the amount of fouling is not objectionable, the pro-
portion of sulphur is increased; and, since the gradual
evolution of a large volume of gas rather than a large
amount of heat is required, the proportion of nitre is dimin-
ished, while that of charcoal is increased, so as to yield CO
rather than CO,. To further delay the combustion the in-
gredients are often mixed, rather than incorporated.
XVI. — PROJECTILES. 45
Bore.
The bore is necessary to provide a large surface of initial
combustion. In order to maintain a uniform pressure
throughout the flight and so avoid either excessive strength
and weight of the case when, at first, the pressure is low;
or a deficiency of strength when, by the increase of the
surface, the pressure increases, the composition should burn
on a surface which is nearly uniform.
To prevent its burning on a decreasing surface, the com-
position must be so tightly packed within the case that the
flame cannot pass around it.
The conical form increases the initial surface without
increasing either of the above objections. Jt also facilitates
the withdrawal of the spindle and increases the strength of
the composition at the section corresponding to the immov-
able layer in a gun. Chapter VII, page 1.
Vent.
The momentum of the rocket is proportional to that of
the escaping gas. The velocity of the gas will increase with
the pressure, and this will increase as the size of the vent
diminishes. The longitudinal and the cross sections of the
vent must be so chosen that the gas will escape as fast as it is
formed, or nearly so, otherwise the velocity of the rocket
will be diminished and it may burst. See Chapter XI,
page 8.
The excess of the total pressure on the head of the bore
over that on the base, and the diminishing mass of the
composition accelerate the motion of the rocket until the
resistance of the air is equal to the propelling pressure: the
variation in velocity will then be slight. When the gas
ceases to flow the rocket becomes an ordinary projectile.
Guiding Principle.
The propelling force of the gas acts always in the direc-
tion of the axis of the bore; it follows, therefore, that with-
46 XVI. — PROJECTILES.
out some means of 'giving stability to this axis, the path
described will be very irregular; so much so at times as to
fold upon itself. Instances have been known when rockets
have returned to the point from which they started. Stead-
iness of flight is obtained either by a guide stick, or by
rotation.
The guide stick is used for signal rockets. It consists of
a long wooden stick affixed to the case so as to bring the
center of atmospheric pressure well in rear of the center
of gravity. Any tendency to deflection is resisted by the
atmospheric moment.
The Hale rocket, figure 26, owes its stability to rotation
produced by the escaping gas. As this expands on escaping
through the vents, it presses against the concentric y^<?;?<r^i-, F^
partly surrounding each of the three vents, and so causes
rotation.
The effect is increased in Macdonald's Hale rocket by a
similiar arrangement in front. In this rocket the bore
extends throughout the composition.
General Remarks.
The difficulties found in constructing rockets so as to
prevent the shrinking of the composition from the walls of
its envelope; their inaccuracy, and their low capacity as
vehicles of kinetic energy have limited their use m recent
times to incendiary purposes, particularly in savage warfare.
Where transportation is difficult and the enemy dwells in
huts of an inflammable nature, as in Africa, the portability
of these weapons causes them still to be retained by the
British service.
Rockets are also much used for transferring life-lines to
the crews of wrecked vessels, and may be applied to the
movement of floating torpedoes.
Rockets are fired from inclined troughs or tubes.
The 12 pounder rockets of the following named varieties,
XVI. — PROJECTILES. 47
fired at an angle of elevation of 8° 15', gave the following
mean ranges and mean lateral errors (for the definition of
these terms see Chapter XXX, page 24) :
Range. Mean lat. error.
Hale rocket 1312 yards. 37 yards.
McDonald-Hale rocket... 2012 . " "
XVII. — FABRICATION OF ARTILLERY PROJECTILES.
CHAPTER XVII.
FABRICATION OF ARTILLERY PRO-
JECTILES.
The fabrication of projectiles involves reference to the
principles of founding, some knowledge of which is neces-
sary to a practical education.
Founding, or as it is less properly called, castmg, may be
divided into three parts, viz.:
I. Molding : by which a cavity, or ??wldj is formed to re-
ceive the molten metal; II. Melting; III. Pouring.
I. MOLDING.
Material of Mold.
Metallic.
When the metal to be cast is fusible at a low temperature,
so that it will remain liquid for some time after contact with
a metallic surface, the mold may be made of a less fusible
metal. This permits great exactness in the resulting casting,
particularly if the metal does not contract much in cooling,
and it allows the mold to be repeatedly employed." For
such reasons the molds formerly used for making bullets,
and those now employed for making fuze-cases of pewter,
and for printing-type, are metallic.
Metallic molds are also used in casting ingots that are to
be forged, and for chill castings, as explained in the Chem-
istry and hereafter.
Non-metallic,
But when the metal to be cast cools so quickly on contact
with a metallic mold that it is apt to set up considerable
2 XVIT. — FABRICATION OF ARTILLERY PROJECTILES.
internal strain; when it is apt to form blow-holes; and par-
ticularly, when its temperature is so high as to be destruc-
tive to the mold, this must be made of sand.
Because of its refractoriness, the sand used is generally
silicious; and to increase its porosity to the gases, and its
cohesiveness, that which is angular and of moderate size is
preferred. Sand also yields slightly to the change in form
of a casting while cooling. For example, a dumb-bell, cast
in an iron mold would probably pull in two, from longitud-
inal strain.
Sand possessing all the properties to be desired for
molding is seldom found in a natural state. Accordingly,
artificial molding co77ipositions are made by mixing sand
with various proportions of clay or flour to increase its co-
hesiveness; or with some combustible material such as coal
dust, horse manure or straw, to increase its porosity at a
high temperature.
The addition of water is necessary to give plasticity; but
as this causes blcw-holes, and even dangerous explosions to
occur, as little of it as possible is employed. In some cases
it is removed h^j drying the mold; or, when great strength
is required^ by baking it.
Molding Compositions.
The presence of water or of a combustible material in the
molding composition exercises an important effect upon the
casting. In both cases the gases resulting from contact
with the molten metal act, as in the familiar example of
water in the spheroidal state, to prevent close contact
between the fluid metal and the particles of sand. The
effect of this contact woujd be to make a rough, gritty
surface, destructive to cutting tools. The combustible may
be incorporated with the sand or applied upon the surface
of the mold.
XVn. — FABRICATION OF ARTILLERY PROJECTILES. 3
^lolding compositions are divided into three classes: —
1. Green Sand, which is wholly or nearly in its natural
condition, and slightly damp. This is principally used for
low grade castings, often molded in the floor of the foundry
so as to avoid the use of flasks.
2. Dry Sand, which is artificially dried after molding.
This is used for cylindrical objects, cast vertically, as it per-
mits a freer escape of gas than does the green sand. It is
also used for castings of copper and brass on account of
their greater conductivity, the object being to prevent their
iooling as rapidly as in the moist green sand. For cohesion,
a certam proportion of clay is mixed with the fresh sand ;
and to compensate for the absence of water and the incor-
porated carbon, sand which is of a fine grain is employed to
give a smooth surface to the casting.
3. Loam. This consists of a plastic mixture of clay
and sand, to which straw, etc., are added for porosity. It
is used for forming large volumes of revolution by the
operation of sweep moldings to be described. Such objects
are cast in pits, and hence the old sand resulting is called
pit sand.
Besides these there are ^v[\^^\o'^Q^^ parting sand 2^x\A facings.
The former is lighter in color and of a finer grain than that
employed in molding, and particularly free from moisture.
Facings are generally composed of carbonaceous material,
such as black wash, a mixture of finely ground coal and water,
or of dry flour, soot, etc. ; though chalk is sometimes em-
ployed on account of the CO^ it gives out when heated.
Patterns.
These are of two classes, according as they have a solid
or a hollow form. The former may be called positive, and
the latter negative patterns. As each kind of pattern is
intended to produce its like in metal, the positive pattern is
4 XVII. — FABRICATION OF ARTILLERY PROJECTILES.
used to form a negative mold, and the negative pattern, or
core box^ to form a positive mold or core.^
To indicate in the mold the position which is to be occupied
by the core, core prints are made on the surface of the pattern.
These form cavities in the sand into which fit corresponding
projections on the core.
Positive patterns require to be made somewhat larger than
the casting; the difference being determined by the shrinkage
of the metal in cooling from the temperature of solidification
to that of the atmosphere.
To facilitate their withdrawal from the sand, patterns are
given a smooth taper surface; the difference in diameter is
called the draught. This requirement influences the number
oi parts in which a pattern shall be made.
Parting Plane.
The parting plane is that in which the main sections or
parts of the mold unite. The number of parts depends on
the choice of the parting plane. Thus, for a rod of elliptical
section, figure 7, if the parting plane contains either of the
principal axes, AB, CD, there will be but two parts. But if
the parting plane contains an oblique axis, as EF, either the
mold or the pattern must be further subdivided.
The parting plane is accordingly taken so as to include
either the maximum or the minimum diameter of the pattern.
Long cylindrical pieces are therefore parted on an axial
plane, as this direction gives them abundant draught.
The parting plane is the plane of reference for most of
the operations of molding.
Negative patterns part on an axial plane to facilitate the
withdrawal of the core, which is often made truly cylindrical,
or of a form not readily admitting ef its withdrawal in the
direction of the axis.
* This distinction is introduced only for purposes of instruction; th«
©rdinary clfissifigation being simply, patterns and corgi.
XVII. — FABRICATION OF ARTILLERY PROJECTILES.
Material.
The material of which a pattern is made depends upon
the number of times which it may be employed, and some-
what upon its size. If made of wood, it should be built up
of pieces having the grain running in different directions so
as to prevent its warping.
In some cases where large castings are made by sweep
moldings the expense of patterns may be spared, and the
necessary concave and convex surfaces of revolution formed,
by templets revolving about an axial spindle. The differ-
ence of radii between the core and the mold so formed
determines the thickness of the casting.
Flask.
The sand forming the mold is supported by an outer frame
or box, called the flask. As many separate flasks are used
as there 2iX& parts in the mold.
For ordinary molding a two-part flask suffices; the part
uppermost in casting being called the cope, and the lower
part the drag.
Lateral motion between the parts of the flask is prevented
by dowels, and the cope is prevented from rising under the
hydrostatic pressure of the melted metal by weights or
clamps, or flanges bolted or keyed to the sides of the drag.
The flask should conform to the general shape of the
casting so as to avoid great differences in the rate of cool-
ing and to facilitate the operations of molding. It often
contains cross pieces to support the sand.
For loam castings, the flask may consist of a pit, sunk
beneath the surface of the foundry floor.
Together with the flask is used^ as a temporary bottom,
the folloiu board. This may have a plane surface next the
flask, or may contain in relief one or more patterns so placed
as to determine the proper position of the corresponding
molds.
6 XVII. — FABRICATION OF ARTILLERY PROJECTILES.
Molding Tools.
These consist of shovels, watering pots and sieves for
mixing the sand; rammers for packing it around the pattern:
trowels of various forms for repairing imperfections, porous
bags containing parting sand and facings, and venting wires
with which to open an escape for the occluded gases.
„ , II. MELTING.
Metal.
The properties of the metal employed depend on the size
of the casting and the nature of the projectile.
A decided advantage in tenacity follows the use of a large
proportion of gun-steel scrap.
The higher the grade of iron, the stronger it is; but the
less fluid it is when melted, and the greater is the shrinkage
and the difficulty of subsequently reducing it to finished
size. The effects of shrinkage are relatively greatest in
small molds.
Consequently for field projectiles grey iron is used, and
for those of larger size that which is more mottled or con-
tains a larger proportion of white iron. For chilled shot a
mixture is made of charcoal and anthracite pig irons, or of
old shot and car wheels in about equal proportions. The
components first named in each pair give toughness, and the
latter the desired hardness to the casting. Car wheels are
cast in chills surrounding the tread, while the centers are
cast in sand. The chill gives hardness where abrasion is to
be feared, and the sand causes the interior to cool more
slowly, thus converting it into grey iron and giving it the
softness and toughness required. The same principle is
applied in the chill casting shown in figure 6.
Furnaces.
The cupola, or the reverberatory furnace is employed
according to the quantity and quality of the projectiles;- to
be cast.
XVII. — FABRICATION OF ARTILLERY PROJECTILES. ?
III. POURING.
To diminish the shrinkage the iron is poured at the lowest
temperature consistent with fluidity; and to make the shrink-
age uniform, small ladles filled from the furnace are pre-
ferred to the large ladles used for great castings.
The melted metal is skimmed while pouring.
FABRICATION OF PROJECTILES.
To apply the preceding principles we will explain the
manufacture of the 4.5 inch shot and shell of the Butler
pattern, referring to figures 1 to 6.
Patterns,
The parting plane is taken at the junction of the body of
the projectile and the tenon for the rotating ring; concen-
tricity of these parts being secured by an axial dowel.
The diameter of the cylindrical portion is enlarged rela-
tively to the maximum diameter of the head; so that, during
the reduction of the body to its finished size, the curvature
of the head near the front bearing shall not be distorted.
For the shot a teat provides a small surplus of metal near
the point and ensures a full casting there. The teat is after-
wards turned off to the curvature shown in the dotted lines.
The shell pattern has a projecting spindle as a core print.
This terminates at « in a conical surface, so that in spite of
wear and unavoidable variations in manufacture it may be
accurately centered in the cross piece,/, of the flask. Such
conical bearings are frequently used in construction.
As it is difficult for the sand to penetrate the small annular
cavity above the main portion of the core, this is separately
formed in the mold box ^ figure 4, before the spindle is seated
in the core box. The mold box represented is of wood,
constructed on the same plan as the core box.
For a double-walled shell the core is covered with a cast
iron corrugated sleeve of the form desired. The resistance
8 XVn. — FABRICATION OF ARTILLERY PROJECTILES.
which this offers to the contraction of the metal about it,
explains why this ingenious form of projectile is not more
largely employed.
The patterns for the gate^ by which the melted metal is
admitted to the mold, and the riser, by which the air and
scoriae escape, are plain conical sticks, sometimes, as in figure
6, made in two parts to facilitate their removal.
Core Box.
This is of iron, made in halves uniting on an axial plane.
It is bored out when bolted together through the four holes
shown, and brought into correct opposition by the four
conical dowels near the holes.
To form the core, an iron tube, called the spindle, per-
forated with many holes and provided with a conical bear-
ing as at a, (all figures,) is wrapped with tow and secured in
the core box by a nut, n. Sand is then rammed around the
spindle, the final form of the core being given by the cup, ^,
so shaped as to strengthen the base of the shell.
Flask.
For large projectiles this is cylindrical; but for small ones
it may be of rectangular cross section so as to contain several
molds. For molding shell or cored shot, a cross piece, /,
figures 5 and 6, containing a conical cavity, is so fixed in the
flask that the parting plane of the pattern shall fall in the
parting plane of the flask. For some projectiles, admitting
of complete perforation, two cross pieces are provided. In
such cases the conical bearings are not required.
To give greater strength to the flask and to preserve the
concentricity of the projectile the parting plane is one of
right section.
Position of the Pattern in the Flask.
Shot are cast point down, so as to give density to the
point-
XVII. FABFICATION OF ARTILLERY PROJECTILES.
Casting shell point down leads to porosity and weakness
of the base which may cause them to fail in the gun. But
when a front fuze is used, as in figure 5, if the shell were
cast point up, the feeding of hot metal from the riser against
the thinly protected spindle would soften it and cause it to
bend. This objection does not apply when the fuze is in the
bottom of the shell.
On account of the difficulty of handling heavy chills^
chilled shot are always cast point down. To prevent the
wear of the chill from the hot metal, which limits its life to
about 50 casts, removable linings are employed. Following
the general principle which requires a symmetrical arrange-
ment of the parts of the mold, and to prevent its cracking
from unequal expansion, the exterior of the chill should
follow the profile of the mold.
Gate and Eiser.
For large projectiles, figure 6, the gate enters the mold
preferably from below, so as to avoid splashing, and tangen-
tially, to give a rotary motion to the ascending column of
metal, and so sweep the scoriae away from its axis.
The riser is intended: —
1st. To allow free vent to the included air and gases.
These are sometimes lighted to assist their dispersion.
2nd. To allow the melted metal to be stirred during the
solidification. This liberates the gases and scoriae; and,
since fused metals are poor conductors, it facilitates simul-
taneous solidification, and thus diminishes internal strain.
3rd. To feed the hot metal into, and sometimes to make
it flow through the mold.
By careful stirring and feeding, shot as large as 12-inch
have recently been cast solid.
Small projectiles may be cast in groups with one gate for
10 XVII. — FABRICATION OF ARTILLERY PROJECTILES.
several molds; but each mold should have an independent
riser.
Large spherical projectiles are sometimes cast in strings^
connected by necks which increase in diameter upward.
OPERATION OF MOLDING.
Secure the spindle of the shell pattern in its seat in the
cross piece by the nut n. Invert the drag so that the shell
shall rest upon the follow board on the parting plane. Place
the main shot pattern upon the point of the follow board
indicated by a dowel. Dust the follow board and the pat-
terns with parting sand. Fill the mold, ramming it suffi-
ciently to make it solid, but not so much so as to unduly
diminish its porosity ; this requires much experience.
Invert the drag, holding it between the follow board and
another board.
Remove the follow board; place the base patterns on the
corresponding bodies and secure the cope by the dowels to
the drag. Dust as before, and fill the mold; inserting the
patterns for the gate and riser at the proper time.
Place the follow board on the cope; lift off the cope and
reverse it; remove the patterns which it contains: they may
require to be slightly jarred, so as to loosen them in the
sand. Do the same for the patterns in the drag.
After repairing, drying, and facing the mold with black
wash or its equivalent, place and secure the core which has
been similarly treated.
Replace the cope and secure it to the drag by such means
as shown in figure 6. The mold is then ready for pouring.
FINISHING.
Preliminary Operations.
As soon as the metal has become sufficiently solid, and
while still hot, and therefore weak, the flask is opened
and the excrescences left by the gate and riser broken
XVII. — FABRICATION OF ARTILLERY PROJECTILES. 11
off. To facilitate contraction about the core the spindle is
withdrawn. This may be easily done, since the tow with
which it was surrounded has been consumed. To retard
the cooling of the casting it is then covered with the
loose sand which formed the mold. When cool, the cavity
is carefully cleaned from sand.
The proper cylindrical form is given by the lathe, the
most important of all machine tools.
Description of the Lathe.
A lathe is intended to form surfaces of revolution by
causing an object to revolve on one of its axes while it
is acted on by a cutting tool to which motion either along
the axis of revolution, at right angles to it, or in both compo-
nent directions may be given, either automatically or
by hand.
Figure 8 shows a lathe, in which A is the frame, the
upper surface of which is formed in parallel rectilinear
ways or guides. M, is the fixed head stock, in which
revolves the cone pulley P. This may be made to carry
with it the concentric live spuidlCy S, and the face-plate,
F, or may revolve independently of these parts. The
spindle is hollow and carries on its interior the conical
center, C. Its exterior is threaded for the face-plate.
T, is the movable tail stock; it contains the dead spindle,
S, provided with a conical center like that in the live
spindle. The tail stock may be clamped on the ways at
any desired distance from Fj a close adjustment of S
may be made by the screw Z>, which is clamped by the
set screw E.
The slide rest G, the invention of the great English
mechanician. General Samuel Bentham, has been used for
only about a century. To its invention is attributed the
practical success of the steam engine; it having been pre-
viously found impossible to produce truly cylindrical
12 XVII. FABRICATION OF ARTILLERY PROJECTILES.
surfaces of large diameter. The slide rest, carrying the
cutting tool, derives its motion from the rotation of the
live spindle by means of a change gear, H, which connects
the outer end of the live spindle with the feed screw, J.
The feed screw passes through a nut on the lower side
of the slide rest, with which it may be thrown into and
out of gear.
Variations in Speed.
The necessary cutting speed, or the velocity of the surface
in contact with the tool, varies with the nature and diameter of
the material to be turned. The angular velocity of the work
may accordingly be varied by means of the steps on the
cone pulley. A similar pulley above the lathe, with its
axis reversed, receives the power from the main line of
shafting by the driving belt, d, and transmits it to the lathe
by means of the working belt, w. The upper pulley is
mounted on an axis provided with a fast and a loose
pulley, / and /, so that the lathe may be set in motion
or stopped by varying the position of the driving belt.
This arrangement, which is indispensable to all machine
tools, is called a counter-shaft. See figure 9.
Where great power, and therefore slow speed Is re-
quired, the back gear, figure 10, is employed. This consists
of two pinions, a and b, mounted on an axis, c, parallel
to that of the spindle $, and so placed that when a engages
with a toothed wheel, d, which is secured to the spindle,
b, shall engage with one of corresponding size, g, upon
the cone pulley.
To use this, the cone pulley is detached from d, and
revolves freely upon the spindle. The back gear may
then be engaged with g and d. The ratio of the diameters
of ^, b, a, d, indicates the resulting gain in power.
By varying the change gear any desired ratio can be
obtained between the angular velocity of the work and that
Xvit. — ^Fabrication Of artillery projectiles. 13
of the translation of the tool. In this way screws of any
desired pitch may be cut.
Support of Work.
The work may be supported by the conical centers form-
ing the adjacent ends of the live and dead spindles. For
this purpose it is provided with corresponding depressions,
which are called center niarks^ at the ends of the axis
of revolution. As a rule these center marks are left in
finished work, as they permit pieces containing them to be
reworked or repaired. The work, in turning between
centers, is caused to rotate by means of a dog^ figure 11;
the tail of the dog fits in a radial notch in the face plate.
In certain cases when turning between centers is impracti-
cable, one end of the work is secured to the face plate
by means of the chuck. This is provided with three radial
set screws capable of simultaneous operation. See figure 12.
In such cases, and to prevent the springing of long pieces
in turning betv/een centers, an intermediate back rest^ By
figure 8, is sometimes employed.
Uses of the Lathe.
It is evident that the lathe may be used for boring as
well as for turning external surfaces, and that by the use
of a hook-shaped tool, passed through the fuze hole,
such cavities as that of the shell can be turned.
Also, that plane surfaces can be formed by omitting the
longitudinal translation of the tool, or that, preserving this
motion and guiding the tool by means of a template,
any desired surface of revolution may be exactly repro-
duced.
By replacing the center in the live spindle by a suitable
tool, against which the work may be pressed by the back
spindle, also without its center, the work may be drilled.
If the tool be made after the manner of a very thick
circular saw, the edge of which may be either cylindrical
14 XVII. — FABRICATION OF ARTILLERY PROJECTILES.
or form almost any surface of revolution, the work may
be moved along a plane director at right angles to the
plane of rotation, so as to form a new surface composed
of parallel rectilinear elements, and having its cross section
correspond to the contour of the tool. This operation
is called milling; it is of the greatest importance in the
manufacture of fire arms, sewing machines and others in
which the interchangeability of the parts is required. To
the general use of milling machines may be largely attri-
buted the eminence of certain American manufactures.
The principal advantages of machines eniploying the
principles of the lathe depend upon the continuity of
the motion and the ease with which it may be varied.
Final Operations.
Projectiles of soft iron are finished externally on the
lathe, or may be forced by an hydrostatic press through
a circular steel die. The former method is preferred. The
head is not touched, in order that the skin^ which is the
hardest part, may remain intact.
Chilled shot require special treatment by a grindstone
or a peculiarly shaped prismatic tool, figure 13. This
forms a scraping, instead of the paring edge generally
employed; it is less apt to spring away from the work
on meeting any portions which are excessively hard, and
may be easily and accurately sharpened by a cylindrical
grindstone.
The natural silicious sandstone is frequently replaced
by an artificial stone composed of emery concreted by a
cement.
FABRICATION OF STEEL PROJECTILES.
Those are intended for piercing armor. Either cored
shot or shell are employed. They may be either cast or
3tvn. — Fabrication op ARtiLLERY projectiles. 15
forged, The former are the cheaper; the latter, so far, the
stronger.
Steel Cast Projectiles.
A rather silicious metal is preferred. In order to fix the
carbon, both head and body are cast in a chill mold; this is
surmounted by a sand mold containing the sinking head.
After cutting off the sinking head, the projectile is hardened,
the point being heated most. It is cooled by first dipping
the point in water and then immersing the whole projectile
in oil. In order to further soften the base so as to permit
the screw thread in the fuze hole to be cut, the base is an-
nealed while the point is kept in running water. To avoid
this operation, the base of the projectile may contain a piece
of wrought iron pipe, around which it has been cast, as in
chilled shot.
Forged Steel Projectiles.
These are hammered into shape from bars of suitable size,
turned inside and out, and hardened and tempered as above
described.
Steel shrapnel are now (1891) economically made by elec-
tro-welding. Chapter XV, page 23.
ROTATING BANDS.
Copper is preferred on account of its softness and strength
and its resistance to erosion by the gases. Its uniformity is
increased by adding about 5 per cent of zinc. This forms
an alloy known 2,% gilding metaiy used in the manufacture
of cartridges, cheap jewelry and the bell buttons used in
the Cadet uniform.
The bands are applied in two general ways.
I. In Casting.
1. The band may be cast in place on the projectile. This is
the simplest plan, but does not always make a good casting.
2. An annular band, the cross section of which is as shown
16 XVII, — FABRICATION OF ARTILLERY PROJECTILES.
in figure 14, is placed in the bottom of the mold before the
metal composing the body of the projectile is poured. To
keep it from melting, it may be surrounded by a much thicker
band of the same material, or by a hollow band through
which runs a stream of water.
II. After Casting.
A seat for the band of the undercut section shown in
figure 15, is turned in the body of the projectile and the band
forced into this groove by hand or by machine.
. 1. By hand.
In this case the band may be either a straight rolled strip
with bevelled ends, as seen in figure 16; or for large pro-
jectiles it may be cast in the form of a semi-circular hoop.
In both cases the placing of the band is done gradually by
the hammer.
2. By machine.
The band complete is slipped over the projectile until
opposite its seat; it is then set in by powerful presses acting
radially.
INSPECTION AND PROOF OF PROJECTILES.
Comparison.
It can hardly be too strongly insisted upon that the in-
spection, not only of projectiles; but of powder and of arms
of all kinds is only preparatory for and subordinate to, the
proof. The inspection may detect the causes of failure in
proof, and often applies to many more articles than can be
profitably proved; but that it can not wholly replace it, is
proverbially and actually true.
INSPECTION,
Object of the Inspection.
The object of the inspection is to detect defects of work-
manship and material which may affect the successful oper-
ation of the projectiles.
XVII. — FABRICATION OF ARTILLERY PROJECTILES. 17
As it is impossible to make all projectiles of exact dimen-
sions, certain variations are allowed in manufacture. For
sake of economy, the greatest variation or tolerance^ con-
sistent with safety and efficiency, should be allowed; both in
workmanship, as shown by the gauges, and in the material.
This remark is general.
Instruments.
Maximum and minimum ring gauges, see Chapter IV, page
11; a hollow cylinder gauge, five calibers long; a profile
gauge; a rolling table, and calipers for measuring the
thickness of the metal at the sides and bottom of the cavity
are the principal instruments required. Besides these there
are various gauges to verify the dimensions of the fuze
hole, and of the rotating device and its seat. Also various
tools for exploring suspicious cavities or defects.
An easy method of detecting small differences in the
diameter of cylindrical holes consists in the use of a
slightly conical bar of steel, the diameter of different
sections of which is marked upon its length after the
manner of a diagonal scale of equal parts.
Except for the rolling table, the names of these instru-
ments and their appearance as represented, figure 17,
sufficiently indicate their employment.
The rolling table is of iron with two parallel ribs at a
distance apart slightly less than the length of the cylindrr-
cal portion of the projectile. These ribs are brought truly
level, so that a concentric projectile will assume a position
of equilibrium of indifference.
Process.
The presence of fissures in hollow projectiles may be
detected by exposing them to an internal jet of steam, or by
observing whether after plunging them in water, notable
differences in the rate of drying occur.
When it is possible, the quality of the material is tested
18 XVII. — FABRICATION OF ARTILLERY PROJECTILES.
by a specimen cut from the body of a projectile. For
chilled shot this is not possible; so that a cast specimen
may be tested and compared with those mixtures which
have given good results. A certain proportion of such
projectiles are also split so as to expose the chill. The
homogeneity of such shot is also tested by striking them
with a hammer at the junction of the body and head: a
clear sound should be produced. In spite of the inspec-
tion, such projectiles are liable to split spontaneously from
internal strain.
In order to stimulate the contractor to greater care,
projectiles are inspected in lots^ the failure of a certain
proportion of which for defects of material suffices to
condemn the entire lot. This is then permanently marked
so as to prevent its being again presented for inspection.
This rule is applied also to defects in workmanship when
the number of objects is too great to permit of the inspec-
tion of every one, as in the ammunition for small arms.
PROOF OF PROJECTILES.
Careful inspection generally suffices for all but those in-
tended for use against armor. But in all cases it is more
conclusive to supplement this by a proof, as by firing for
accuracy.
Armor piercing projectiles are proved by firing about one
per cent of a lot against wrought iron armor about one
caliber thick ; the chilled iron striking normally and the steel
at about 20 degrees to the normal. Upon the performance
and endurance of the proof projectiles, fired with penetrating
charges, depends the acceptance of the lot.
XVIII. — MEANS OF COMMUNICATING FIRE.
CHAPTER XVIII.
MEANS OF COMMUNICATING FIRE.
These may be divided into two classes, viz.;
1. Those intended for igniting stationary charges in guns
and mines. It includes various forms of matches and
primers.
2. Fuzes, which are intended to be used in moving objects,
such as explosive projectiles, torpedoes, etc.
CLASS I.
MATCHES AND PRIMERS.
According to the time elapsing between their own igni-
tion and that of the charge, these may be considered as
relatively slow or rapid.
IGNITERS COMPARATIVELY SLOW.
Slow-Match,
This was formerly employed for igniting the port-fire,
by which the loose gunpowder priming laid around the
upper orifice of the vent was fired. It is now employed
only for preserving fire. If made of hemp rope, combustion
is retarded by saturating it with lead acetate, or the lye
of wood ashes. If of cotton it is only necessary that
the strands be well twisted. Slow match burns from 4
to 5 inches per hour.
Quick-Match is used to communicate fire, as in fire-works
and in experimental work of a dangerous character. It
is made of candle wick, steeped in a mixture of mealed
8 XVm. — MEANS OF COMMUNICATING FIRE.
powder and gummed spirits, wound on a reel, dredged
with mealed powder and left to dry. ^t burns at the rate
of about 3 inches per second.
Varieties of duick-Match.
The rate of burning may be much increased by enclos-
ing the quick-match in a paper tube; see Chapter VIII.
If, instead of paper, the envelope be made more pliable
and strong, as by a spiral wrapping of cloth around a
central core of fine powder, the ordinary blastings or Bick-
ford fuze results. This inflames at a less rapid rate than
the kind just named.
A tube of lead or one of its alloys may replace the
weaker envelopes above described and instead of simply
fitting it closely, the tube, enclosing the core, may be
drawn as one mass after the manner of wire.
If gun-cotton be used for the core, a most convenient
and rapid form of detonator results.
IGNITERS COMPARATIVELY RAPID.
Caps and Detonators.
These consist of cups or tubes made by means of a
double punch, figure 1, the inner member of which, /,
passes through a conical hole, h, of somewhat larger diam-
eter in a stationary piece, d^ called a die. The outer
punch,/', which is concentric with the inner and fits closely
to it, as it descends into a shallow cylindrical depression
at the mouth of the die, shears from a thin copper ribbon a
disc which it holds by the edges while the inner punch forms
it into a cup. The elasticity of the cup causes its open end to
expand as soon as it has passed through the die : this strips
it from the punch as the latter rises for another stroke. The
cup is elongated into a tube by the successive operation of a
series of single punches and dies of gradually decreasing di-
ameter, See plates Chapter XXVII, This operation, which
XVIIl.— MEANS OF COMMUNICATING FIRE. 3
resembles closely that of rollings in chapter XV, is of great
utility in the arts. For military purposes it is principally
used in the manufacture of metallic cartridges.
For percussion caps for small arms, the tube receives
a charge of moist fulminating composition. This is pre-
vented from falling out, when dry, by a disc of tin foil,
held in by varnish.
The construction of the detonator has already been
described in chapter XIV.
Cannon Primers.
These are of two classes, according as they are fired
by friction or electricity.
I. Friction Primers.
The friction primer presents the following advantages
over the method of firing cannon described, page 1. It
is portable, certain and rapid; it affords the means of firing
pieces at a distance, and does not attract the attention of
the enemy's marksmen at night.
According to the direction of the vent, friction primers
are divided into two classes.
I. Radial Vent.
The primer used in the military service of the United
States consists of two copper tubes, soldered at right angles
to each other, figure 2.
The short tube contains a charge of friction composition,
(Sbg S3 and K CIO3) inserted moist and surrounding the
roughened end of a wire, the outer extremity of which
forms a loop for the lanyard. The long tube is filled with
fine powder, retained by a wad of wax. The nib of the
wire is folded over the end of the short tube, so as to
prevent its accidental displacement and the firing of the
composition in consequence.
For large guns, the column of fine powder may surmount
4 3^\ltt.--MEAMS OJ* CoMMttNlCATmc MVlU.
a pellet of compressed powder which will be shot, burning,
into the cartridge.
In some services the cross tube is omitted and the wire,
inserted axially, is withdrawn by a motion which causes it to
bend continuously around the edge of the vent. See
figure 3.
2. Axial Vent,
As the discharge serves to expel the empty tube with
great velocity, unless it be thrown upward it may injure
the bystanders. On this account, and also to prevent the
erosion of the vent by the escaping gas, an ohtwating prbner
is screwed into a proper seat concentric with the vent.
Figure 4 represents an obturating axial friction primer.
When the wire is withdrawn, the conical portion, c, finds
a corresponding seat at the end of the cavity surrounding
the wire. This prevents the escape of gas through the hole,
while the escape around the primer is prevented by the
radial expansion of the thin edge in which the portion
nearest to the charge is formed.
The stop, ^, prevents the primer from being screwed in
too far, and the enlargement, ^, serves a similar purpose for
the wire.
II. Electric Primers.
These are used for firing charges at a considerable
distance, as in certain cases in modern warfare when the
gun is so protected that the object is invisible from its
neighborhood; so that the pointing and firing are controlled
by a distant observer. By this means also, the simultaneous
discharge of several cannon at a common object may
greatly increase their effect. A similar advantage follows
in mines.
The primers are of two general classes:
I. High tension, in which ignition results from the pass-
age of the electric spark between the disconnected ends
XVIII. — MEANS OF COMMUNICATING FIRE. 5
of two insulated conductors. For this class the conductors
require careful insulation and to be separated from adjacent
circuits, so as to prevent the primers in one circuit from
being accidentally exploded by currents induced from the
other circuits.
2. Low tension^ in which ignition results from the heating
of a short wire of high resistance which connects the ends
of the conductors. Owing to the ease with which the con-
dition of the circuit can be tested before firing, and the
comparatively low electro-motive force of the currents
employed, this is the only class of electric primer used
in artillery.
Figure 5 represents a common electric primer, and figure
6 an obturating electric primer. The platinum wire is
coiled to facilitate its handling in manufacture. It is sur-
rounded by a wisp of gun-cotton.
The obturating plug,/, of hard rubber seals the channel
by being pressed against the sharp ring in rear. In other
essentials these primers resemble figures 2 and 4:.
MEANS OF IGNITING PRIMERS.
If quick match be used it sufiices to unite the lines so
that the distances B C, B C, B C\ etc., in figure 7; or
BC^ B D C, figure 8, be equal. If the detonating tubes,
page 2 be used, these precautions are unnecessary.
For electric primers the voltaic battery is generally
employed, although for experimental purposes a small
portable dynamo or frictional apparatus is very convenient.
When it is desired to be able to fire without delay, a
battery is preferred, which, like the Leclanche, can be kept
for a long time in open circuit without sensible change and
which only needs the circuit to be closed to produce the
effect desired.
In using the electric current in direct or continuous circuit
6 XVIII — MEANS OF COMMUNICATING FIRE.
as in figure 9, the number of cells of the battery required
increases with the number of primers, /,/',/", and it may
happen that the most sensitive of the primers, exploding
first, will cause the remainder to fail.
For the second reason a derived, or parallel circuit, as
in figure 10, is preferred. The successive explosion of the
more sensitive primers increases the current which passes
through each of the remaining primers, since their number
is diminished.
In order to employ a weaker battery, the arrangement
shown in figures 11 and 12, serves, by sweeping the key, ky
over the ends of the terminals, to produce a practically
simultaneous discharge.
CLASS II.
FUZES.
Fuzes are employed to explode the bursting charge of a
projectile at any desired point of its trajectory. They may
be classified, according to their mode of operation, as timey
impact and combination fuzes.
I. TIME FUZES.
A time fuze contains a column of com.position, which,
having been ignited at the discharge of the piece, after having
burned for a definite time, ignites the bursting charge.
Requisites.
Such fuzes are principally employed to burst projectiles
while in the air; they therefore require that the relation be
known between the distance to the point of explosion and
the time of flight, and that the column be taken of such a
length that it will burn in the time so determined.
The first of these requisites involves the estimation of the
distance by various systems of range finding, and the deter-
XVIII. — MEANS OF COMMUNICATING FIRE. 7
mination from Ballistics of the required angle of projection
and the time of flight to the point desired. The second
requirement demands that the rate of burning be known,
and, since the time of burning is varied by varying the
length of the column, that the rate be uniform throughout
its length. Finally, that the column be taken of the exact
length required by the rate, and that it both receive and
impart fire with certainty.
The principal points to be considered in the development
of time fuzes are, that as we increase the muzzle velocity
and sectional density of our projectiles, the longer will be
the maximum time of burning required for the fuze. As
the remaining velocity increases, the greater will be the error
in distance due to a given error in time; and the greater the
range, the more difficult will it be to detect the error in
distance. Therefore improvements in cannon require corre-
sponding improvements in the uniformity of rate and in the
exactness of the length of the burning column. The greater
the rate of burning, the larger the scale and therefore the
smaller the effect of a given error in cutting.
The rate is so much affected by the conditions relating to
the resistance of the air during flight, that, while uniformity
of rate may be indicated by the tests of manufacture, the
lengths of column for given ranges should be determined by
actual trial in the gun. On this account, and to avoid com-
putation in the field, when the initial velocity and sectional
density are fixed, the scale is preferably one of ranges, in-
stead of units of time.
The great efficiency of projectiles properly exploded in
air, as explained in Chapter XVI, and the experience gained
with smooth-bore cannon, in which this was the only form
of fuze that could be successfully used, account for the pains
that have been taken to meet these requirements ever since
the early days when the fuze was lighted before loading.
8 XVIII. — MEANS OF COMMUNICATING FIRE.
Kate of Burning.
This will depend upon the conditions named Chapter
VIII, page 3.
The rate was formerly varied by varying the composition,
but as any departure from the usual proportions is found
to diminish the uniformity of the rate, to increase the
difjficulty of preservation, and to increase the amount
of residue, it is now thought best to vary the rate only
by varying the amount of incorporation and the density
of the composition.
When the total time of burning is very great, as in some
of the large mortar projectiles, which may be 40 seconds
in the air, a return to the variable composition appears
necessary.
Former Practice.
For spherical projectiles the column was cylindrical and
was ordinarily contained in a conical case of paper, wood or
metal. This was filled with small successive quantities of
mealed gunpowder which were compacted by a drift upon
which a given number of blows were struck by a mallet. By a
repetition of the process the case was gradually filled.
The exterior of the case was divided into equal propor-
tionate parts by which to regulate the time of burning,
either by cutting off the case; or, since the entire column
might then be dislodged backward into the cavity of the
shell by the shock of discharge, by boring into it with a
gimlet.
The fuze was ignited by a priming of mealed powder
placed so as to catch fire from the flame passing through
the windage of muzzle-loading guns, both smooth-bore and
rifled.
The method of filling caused variation in fuzes of the same
kind, and even between different sections of the same fuze.
\ XVIII. — MEANS OF COMMUNICATING FIRE. 9
1 ' ~
\
Exv.mples of Fuzes for Muzzle-loading Projectiles,
Figures 13 and 14 illustrate two varieties of time fuze, in
one of wUch the composition was fixed in the case and in
the other v^as movable.
The Mortar fuze case or plug was made of a close grained
wood, like beech, bored out nearly to the bottom. The
top of the cavity was enlarged to receive the priming of
mealed powder and alcohol. This was covered by a cap
of waterproof paper on which was marked the rate of burn-
ing. For economy of manufacture the exterior of all
mortar fuze plugs was marked in inches and tenths, instead
of with reference to the rate of burning of their contents.
The Sea Coast fuze consisted of a brass plug containing
a separate paper case, filled with a composition of variable
proportions and bearing on its exterior a scale of times.
The mouth of the plug was closed by a water-cap, per-
forated by a zig-zag channel. This was also filled with
mealed powder for the ignition of the fuze; but was so
constructed as to prevent the composition from being
extinguished in the ricochet fire over water, largely em-
ployed in former times.
These fuzes answered well for the comparatively low
remaining velocities and short ranges usual when spherical
projectiles were employed; but they required valuable time
for their adjustment and were imperfectly protected from
the effects of excessive heat or of moisture while in store.
The Bormann fuze, figure 15, was invented to overcome
these and other objections. The case being of pewter is un-
altered in size by meteorological changes, and it contains
the composition in a channel, which, though air tight, can
be readily cut by a proper tool. The circular form of the
column and its diminished section allow the size of the case
to be reduced, and the composition to be compressed in the
direction of its shortest dimension. The mean density of
10 XV^I. — MEANS OF COMMUNICATING FIRE.
the succe^ssive layers estimated in the direction of the com-
bustion is thereby made uniform. The case is screwed into
the fuze hole by a screw driver, the prongs of whxh engage
into the recesses a, a.
The graduated arc lies over the circular column of
mealed powder which, after compression, is covered by the
tightly fitting wedge shaped ring, b. The only outlet to
the channel is under the zero of graduation; this outlet, r,
and the magazine^ m, are filled with fine powder which is
retained by a disc of tin, e.
To enable the fy^e to resist the shock of discharge, to
which its softness, density and form render it especially
weak; and also to increase the effect of a small bursting
charge, the lower portion of the fuze hole is closed by a
perforated disc,/.
The objections to the Bormann fuze are the short time
of its burning; the uncertainty of its ignition unless it
be carefully primed, and that, once set for firing, it is use-
less for any greater time of flight.
Present Time Fuse.
The use of breech-loading cannon necessarily prevents
the ignition of the fuze through the windage so that a special
device called an inertia igniter is employed for that pur-
pose. Its operation is illustrated in figures 16 and 24.
In figure 16 the inertia igniter consists of a mass of lead
containing a pellet of fulminate and supported a short dis-
tance above the sharp point, /, by some device which, while
stable against ordinary shocks, will be surely moved by that
of discharge. This device may be either a spiral spring or a
transverse pin of brittle material.
The flame from the fulminate escapes through the holes^
h, into the annular cavity, r, and, by a hole on the inner
surface of the ring, r, ignites the circular column of com-
position which the rmg contains.
XVIII. — MEANS OF COMMUNICATING FIRE. 11
The exterior surface of the ring is graduated, as in
seconds, and the body of the fuze contains a mark, placed
opposite to the entrance to the magazine, w, so that by-
setting the ring before firing with any division of its scale
opposite to the mark, the length of the burning column is
fixed. The cap, k, is used to c^amp the ring in place.
To prevent the opposing rush of the gases from the two
sections of the burning column, it is ignited at one of its
ends; this permits a free escape of the gases to the outer
air through a hole previously temporarily sealed against
moisture.
Figure 17 shows the course taken by the escaping gases
when the burning surface moves, as in the Bormann fuze,
in two directions from the hole, ^, to the magazine, m^
Figure 18 shows the improved method.
For long ranges, since the form of the projectile permits
its length to be indefinitely increased, the fuze may contain
two or more rings arranged in tiers.
II. IMPACT FUZES.
Concussion Fuzes.
Until the introduction of rifled projectiles many unsuc-
cessful attempts were made to combine the time fuze with
some device which would be safe when the gun was fired;
and yet, if the time fuze failed to act at the proper point,
would explode the bursting charge on impact.
Owing to the uncertainty of the direction of the impact
such fuzes are called concussion fuzes to distinguish them
from the percussion fuzes now generally employed.
Percussion Fuzes.
Although as stated, Chapter XVI, page 21, the shock of
impact may in certain cases suffice to explode the bursting
charge, it is much more certain to employ a special appa-
ratus for this purpose.
12 XVIII. — MEANS OF COMMUNICATING FIRE.
Although more complicated in structure than time fuzes,
those of the percussion class act with more certainty since
the conditions to be fulfilled are more easy of accomplish-
ment. They are not as subject to deterioration in store,
and, since they are usually entirely automatic, they require
no preparation before firing. By the volume of smoke
resulting from the explosion of shells containing percussion
fuzes, the gunner is afforded one of the readiest means
of correcting his aim.
Percussion fuzes are divided, according to their position
on the projectile, into fronts or base fuzes. The former
possess the advantage that on impact, the bursting charge is
thrown towards the fuze ; the latter class is required for pro-
jectiles to be used against armor.
Requisites.
A good percussion fuze requires —
1. A case to hold and guide the movable parts, and to
protect them from being clogged by the dust arising from
the bursting charge in transportation, and by the earth
against which they may strike.
2. A plunger, by the motion of which, on impact, the
charge is fired.
3. A fulminating composition, ignited by the plunger.
4. The priming, a charge of fine powder ignited by the
fulminate and serving to increase the certainty of the
ignition of the bursting charge.
5. A safety device, by which the accidental dislodgement
of the plunger is prevented; but which will certainly free
the plunger when the piece is fired.
6. A device to prevent the plunger from moving forward
in its cavity during flight. This tendency results from the
greater retardation of the projectile than of the enclosed
plunger by the resistance of the atmosphere. The effect
of this relative motion may be to cause a premature explo-
XVllt.— MeA^§ of COMMtJi^lCAftNG FIRE. ' 13
sion if the fulminate is sensitive; or else on impact to
deprive the plunger of sufficient motion to cause the explo-
sion of a fulminate, the sensitiveness of which, for the reason
above given, has been diminished.
The most difficult of these requisites to provide is the
safety device. In the early percussion fuzes the plunger
was a single mass sustained by a transverse pin or by lugs
cast upon it. The pin was made strong enough to stand the
shocks of transportation; but was shorn off by the shock of
discharge. The mass to be given to the plunger was determ-
ined by confficting considerations. If made so light as not
to be liable to shear its support by accident, it might fail
to explode the fulminate when impact occurred at a low
velocity. The advantage of a proper distribution of func-
tions among the parts of the apparatus appears from the
following discussion:
Type of Improved Percussion Fuze.
Let Fhe the initial velocity of the projectile and v, and
z;', its velocities on impact, and after impact, as in the
ricochet.
Let m, be the mass of the plunger and p/ that of the
safety device: this we will suppose to be a hollow cylinder
as in figure 19, surrounding the upper part of the plunger,
but kept from moving backward upon it by a suitable pro-
jection, as that upon the flat spring, s\ In the type selected
the section of the plunger is square and fits the hole in the
safety device.
When the piece is fired, m' moves relatively to the rear
with an energy which, on account of the large value
2i
of Vj is capable of overcoming a resistance great enough to
be absolutely safe against all accidents of transportation.
In so doing it becomes solidly united to m, so that when
impact occurs, although v—v' may be much less than F",
14 Xvm.— MEANS OF COMMUNICATING FIRE.
the energy — - — {v—v'Y may easily overcome the resist-
ance of the spiral springs, and so ignite the fulminate,/,
and the priming,/.
If, during the flight of the projectile m' does not remain
relatively at rest its conical form tends to make it roll
rather towards the base of the cavity than away from it. It
is also urged in this direction by the spring s.
This fuze, which is of French origin, represents one of
the best existing types. It requires a value of V not less
than about 1000/. ^., and therefore is somewhat more com-
plicated in construction when projectiles containing it are
fired with low velocities.
Percussion Fuzes used in the United States.
Hotchkiss Front Percussion Fuze. Figure 20.
A, is the case, closed in front by the screw-cap B, and
with a conical hole in rear closed by a lead safety plug C.
Dy represents the plunger, composed of lead cast into a
brass jacket to prevent its dilatation by shock,
A continuous brass wire, E, the upper portion of which
is bent in a semi-circle concentric with the plunger, is cast
into the lead and supports the plunger in the case. The
lower ends of the wire are securely held by the friction
of the safety plug against the sides of its cavity. At 7% is
the fulminate, and at F, the priming.
When the piece is fired, C, is dislodged backward into
the interior of the cavity either by its own inertia or by the
blow received from F). The wires spread outward and
prevent the plunger from moving forward until the pro-
jectile strikes a sufficiently resisting object.
Hotchkiss Base Percussion Fuze. Figure 21.
The case. A, carries the fulminate, F, in a large percus-
sion cap contained in the perforated screw-box^ which is
XVIII.— MEANS OF COMMUNICATING FIRE. 15
formed in two sections, G and JI. The base of the case is
provided with a projecting flange, /, brought to a thin edge
which, when the fuze is screwed home, acts as a gas check.
The plunger Z>, is made as in figure 20, but contains a
central firing-pin, Z, roughened so that it will hold well
in the lead.
The rear end of the firing-pin projects beyond the bottom
of the plunger, while its front end is sunk a little below the
surface so that when this compound part {D and L) is in
place, it is prevented from moving by the screw-box.
When the gun is fired the plunger slides back on the
firing-pin so that the point projects above the plunger.
The lead being soft, and being prevented from expanding
by the jacket, it takes a fresh hold on the pin and supports
it when it is thrown forward on impact.
This fuze has certain structural defects which render
its operation less certain than that of the front fuze. For
its special purpose it is probably one of the best known.
Krupp Fuze.
Figure 22 shows a Krupp fuze in a double walled shell.
Safety in loading results from the transverse pin, /, which,
with the screw-box containing the fulminate, is inserted just
before loading. The rotation of the projectile expels the
pin, leaving the longitudinal pin,/, free to be driven inward
on impact so as to prevent the entrance of earth into the
cavity of the fuze. The nomenclature of figure 22 is the
same as that of figures 20 and 21. It is said that this
pattern is to be replaced by one containing a safety device
which is intended to be unscrewed by the rotation of the
projectile.
III. COMBINATION FUZES.
These combine the principles of the time and impact fuzes
50 as; —
16 XVIII. — MEANS OF COMMUNICATING FIRE.
1. To increase the probability of explosion; since, if the
probability of a failure in each of the two cases be, say, 0.01;
that of the combination will be 0.0001.
2. To permit the character of the firing to be rapidly
varied,
3. To increase the certainty of explosion when the pro-
jectile is fired with a low velocity.
Figure 23 illustrates one of the most recent combination
fuzes used in the French service.
^ is a leaden fuze tube made as d^escribed page 2. It is
wrapped spirally about, and secured to the hollow cone, C;
this is held in place by the clamp screw, D. The lower end
of the fuze tube communicates through the priming, /*, with
the cavity in which lies the percussion fuze described page 13.
The inertia igniter consists of a loose, pointed piston, ZT,
which, until the instant of discharge, is separated from the
fulminate, F^ by the spiral springs .S".
K^ is a conical cap pierced with a series of numbered holes
corresponding to the times of burning and provided with a
vernier for interpolating a puncture between any two holes.
The puncture, owing to the softness of the metal of which (7,
is composed, is made entirely through both its walls.
When the piece is discharged, the washer of compressed
powder, W^ is ignited by ZT, and through the puncture the
fire extends to the composition in E. At the same time the
percussion fuze acts as before described.
But for the union of the two fuzes in the same case, which
the construction of the projectile and the operation of front
percussion fuzes requires, this fuze illustrates the principle
referred to Chapter XVI, page 34. The simplicity of con-
struction, which was formerly considered of prime impor-
tance, has been entirely subordinated to efficiency of oper-
ation, notwithstanding the greatly increased cost which this
involves.
XVIII. — MEANS OF COMMUNICATING FIRE. 17
The Flagler Combina^tion Fuze. Figure 24.
This fuze, devised by Colonel Flagler of the Ordnance
Department, is now, 1889, undergoing trial. It combines
many of the principles just discussed and adds two new
features to provide for the requirements numbered 5 and
6, page 12.
The first feature consi^s of a copper wire, d^ screwed from
the rear into the open end of the screw-cap^ A. The lower end
of this wire is bent at right angles so as to support firmly
the leaden time plunger, D. Just below the screw thread
by which it is suspended the diameter of the wire is reduced
to any desired extent.
The wire is broken at the neck so formed by the stress
due to the acceleration of the projectile, both in translation
and in rotation. The latter stress, occurring only when the
piece is fired increases the certainty of ignition without
diminishing the safety of the apparatus against accidental
shock.
On firing, the mass, Z>, is thrown against the fixed firing
pin, F^ and the fulminate ^^, is ignited. The flame from
the fulminate escapes through the radial holes and the an-
nular channel, ^, b^ to the end of the column of composition
projecting into the radial groove, Z, formed on the lower
side of the ring, or carcass C. The gas first formed blows
off the vent cover, ^, and allows the remaining gases to
escape freely.
When the column has burned to the point, b\ corre-
sponding to which there is a fixed mark on that portion
of the body next to the graduation on the ring, the priming
K^ is ignited and the flame from it passes down the fluted
surfaces of the members, G^ H^ 7, of the percussion fuze
into the bursting charge.
The advantage claimed for this safety device over those
in which ears projecting from the mass Z>, are shorn off by
IS XVIII. — MEANS OF COMMUNICATING FIRE.
the shock of discharge, refers to the uniformity of copper
wire and to 'the absence of the loose pieces, which, after
shearing has occurred, may impede the action of the
plunger.
The percussion fuze resembles the Hotchkiss base fuze,
with the following advantages: —
1. The priming K, which serves for both fuzes of the
combination, makes the volume of the flame on impact
much greater than when fulminate only is employed.
2. In order to fulfil requirement 6, page 12, a disc of thin
zinc separates the point of the firing pin, h, from the fulmi-
nate above it. This presents a positive and uniform
resistance to premature explosion; and, since a pressure of
6 pounds is required to pierce it, the fulminate may be
made as sensitive as may be desired.
3. On impact the powder is thrown toward the fuze.
The fuze works well in practice. The percussion fuze
was found to operate when the projectile was fired through
a 2-inch board, though it failed in penetrating a board one
inch thick. It is thought that it will explode on striking
animate objects or sandy or marshy ground.
GENERAL REMARKS.
Owing to their greater permanency of form in store, and
their diminished volume, metallic cases are preferred to the
wooden ones formerly employed.
In order to cheapen the manufacture, which at best is
very expensive, the parts are, whenever possible, made of
pewter, cast in metallic molds into finished forms. When
strength and infusibility are required, brass or bronze are
used, cast as described in Chapter XVII.
To prevent unscrewing during flight, the screw thread of
base fuzes should turn in a direction contrary to that of
the rifling.
3tvni. — MEANS O^ COMMttNlCATiNG f'lRE. 19
It takes an appreciable time after impact for tLe explo-
sion to occur; so that even when the fulminate was pur-
posely ignited by the shock of discharge, the shell did not
burst until it had gone several yards beyond the muzzle of
the gun. This is of importance in understanding the effect
of shrapnel fire with percussion fuzes, and serves to show
that explosions within the gun generally result from defects
in the construction of the projectile.
To prevent premature explosion from the plunger's
being thrown violently forward by the elasticity of the
bottom of the shell, on discharge, a perforated cardboard
washer is often required.
A percussion shell, unexploded in experimental firing
should never be tampered with: if possible, it should be
exploded on the spot by a dynamite cartridge.
X15t. — GDN CoKstktrcTioN.
CHAPTER XIX.
GUN CONSTRUCTION.
Nomenclature of Stresses.
The total pressure of the powder gases in a gun may be
analyzed as follows with reference to the direction of the
resulting strains.
1. A radial stress, known by the special name of
"pressure" (/).
2. A tangential stress, or hoop tension (/) which tends
to split the piece open longitudinally, being similar in its
action to the force which bursts the hoops of a barrel.
3. A longitudinal stress ((/) which tends to pull the piece
apart in the direction of its length.
4. Besides these, which are the principal stresses now
considered, was formerly treated the transverse stress which
tends to bend outward the staves of which the tube may be
supposed to consist.
Its effects are so closely associated with the strains above
named that it is no longer discussed.
Of the principal stresses named the most important is the
tangential, since it is that from which failure most readily
occurs.
BARLOW'S LAW.
Limitations.
This law, which was until recently applied to the con-
struction of homogeneous cannon, if confined to stresses
beneath the elastic limit, (Chap. XV, p. 11,) under which
XIX. — GUN CONSTRtJCTIOl^.
limit the stresses are taken to be proportional to the strains,
gives results which agree fairly well with those obtained by
the more exact methods now generally employed.
But, when applied to built up guns composed of concentric
cylinders assembled by shrinkages as described in Chap. XV,
it is no longer generally used because it does not analyze
the resultant strain into the component strains occuring in
three coordinate directions. For example, if we compress a
cube in the direction of the axis of Z, there will be deyeloped
along the axes of X and Y component strains correspond-
ing to tensile stresses acting in each of these directions and
conversely.
On account of the relative simplicity of Barlow's law it
will be employed to illustrate the general principles of gun
construction. A more extended discussion of the theory now
accepted will be found in the appendix of this chapter.
DEDUCTION OF BARLOW's LAW.
Hypotheses.
Suppose — {a) the piece to be a hollow cylinder of homo-
geneous metal, and — {h) that the effect of a central force be
transmitted outward in such a manner as to make constant
the area of cross-section by a plane perpendicular to the
axis.
{a) The homogeneity of the metal Is required, so that a
constant relation may exist between stress and strain ; or that
the coefficient of elasticity, known herein as E^ may remain
constant.
{h) The constancy of area or cross-section resembles
the assumption that the various stresses, from the effects of
which the physical properties of the metal are determined
in the testing machine, continue to be applied to the original
XIX. — GUN CONSTRUCTION.
area of cross-section ; although it is evident that, if the volume
of the metal be constant, its area of cross-section must
diminish or increase when exposed to tensile or compressive
stress respectively.*
Wertheim's experiments show that the developed strains
are each — ^ of the principal strain.
Preliminary Statement.
Suppose that figure 1 represents a section of a homogen-
eous gun after firing: the radii R and >^' having been ex-
tended to r and J^" so as to maintain the sectional area
constant.
Then, the area whose limiting radii are r and E' being
common to both states of the section, we have
TT (r^ _ i?^) rr TT {R" » — R' '), or
(r J^R){r—R) = {R" + R') {R" — R'),
But since R" and R' are each greater than either R or r
R" + R'y r-\-R
,'.r—RyR"^R', or
2 TT{r—R) __ r—R R" — R'
27rie ~". i? -^ R'
The two members of this inequality measure the strains
on the interior and exterior surfaces respectively, so that it
appears that the surface of the bore might be strained be-
yond its elastic limit before that of the outside layers was
reached.
The resulting set, if slight, might destroy the accuracy of
the piece from the dilatation of the bore; and, if consider-
able, it might lead to the formation of fissures which would
*Throughout the following discussion we will consider that we are
dealing with a cylinder of but one unit of length, since, as the length of
the cylinder varies, both the pressure tending to burst the cylinder and
the resistance which it opposes will vary in the same ratio.
XIX. — GUN CONSTRUCTION.
facilitate the final rupture in detail of the successive cylin-
drical layers of which the gun may be supposed to consist*
The considerations explain the statement in Chapter V,
as to strength vs. weight.
Analysis.
To determine the law by which the tangential stresses
are distributed throughout the section of a gun: —
Let J^ and Z be the radius and the circumference of the
bore. Let /<, be the radial pressure per unit of area and
T the tangential stress on the surface of the bore. Let r, Zy
p and / represent the same quantities on any exterior
cylindrical surface, the area of cross-section between which
and Z is A. Then by assumption, {fi) above
Tt {f— B}) ::^ A, and .*. rdr = RdR.
Multiplying the first member of the last equation by -,
and the second member by -^ we have r^ — = i?^ -^ .
'' R r R
I But, since the ratio between the circumference and the
radius is constant, and since beneath the elastic limit the
stresses are proportional to the strains
, dr dz t . dR T
i - = V = ^ ""^ ■:ff = ■:£
Therefore, we have
tf^ TR^ , TR^
_ = — or/=-^ (1)
Or, since under given conditions of /o? ^ and i?, TR^
will be constant, the tangential stress {or strain) on each sue-
* This last statement, though generally true, is subject to modification
depending on the ductility of the material and the development of special
elasticity. See post.
XIX. — GUN CONSTRUCTION.
cessive concentric elementary cylinder varies inversely with the
square of its radius. ' This is Barlow's law.
This condition may be represented by figure 2, in which
the ordinates of the curve T T' represent the tangential
stresses on the corresponding circumferences.
In this figure and in those succeeding it, positive hoop
tensions are represented by ordinates laid off above the line
representing the trace of the axial plane of least resistance,
and negative hoop tensions (compressions) are laid off below
this line. See figures 5 and 6.
RESISTANCE OF THE CYLINDER.,
Bursting Effort.
Imagine the radial pressure on a unit of area, or /oj to be
decomposed into two components/' and/^ figure 3, respect-
ively perpendicular and parallel to the axial plane, O R\
along which rupture tends to occur; and consider but one
quadrant of the bore at a time.
Let cp be the variable angle made by the radial pressure
with the plane O R',
Then, /' =/o sin ^,
and, since,
d Z'=- R d cp^
J)' dZ=p(iR sm cpdcp = —p^Rd cos cp.
n R
Integrating between Z—^ and Z=— -— and the corre-
<)
spending values of cp^ viz. and 90°, and calling P^ the
total pressure on the inner surface of the quadrant perpen-
dicular to the plane of rupture, we have
=/
XIX. — GUN CONSTRUCTION.
And for the force acting on both quadrants to lift the semi-
cylinder from the axial plane, or for the bw'sting effort
%F=p,%R. (2)
This might have been inferred from the fact that the burst-
ing effort is independent of the configuration of the surface,
upon which it acts.
Eesistance.
The bursting effort must be in equilibrium with the sum
of the tangential stresses developed in both quadrants, or
in figure 2.
27'=/o2i? = 2^/=2 X areaierr'J?'
or
A=2--^-. (3)
COROLLARIES. I
1. The maximum permissible value of T\s the elastic limit
of the material under tensile stress. Calling this and repre-
senting by/g the corresponding powder pressure we have
}.=e^. (4)
Equation (4) gives the means of determining the maximum
pressure for a gun of which the corresponding section is
known, or of determining the thickness of which a gun of a
given caliber should be made to resist a given pressure.
2. If guns be similarly proportioned, R' •=znR^ whence
by substitution
/o=^^- (5)
X13t.— CUJ^ C0N§TRt)Ctl6N.
Equation (5) shows that all similar guns of the same material
can resist the same maximum pressure.
In the old cast-iron guns, in which for the reinforce, n was
generally taken equal to 3, or the walls of the gun made
one caliber thick, /o = f ^j i^ the metal be without internal
strain. Chapter XV, page 21.
3. Since < 1, A < 6^ unless i? = or ^' = oo . Or
n
the powder pressure must always be less than the elastic
limit of the material.
4. The curves of figure 4 are constructed from equation 1,
using a constant value of ^'j= 6 and taking 7"= d and
« = 3; 2; f respectively. It is apparent that as n dimin-
lishes the curve T t; T^t^; T' t' becomes more nearly
parallel to O R\ and the area beneath the curve tends to
increase from this cause. On the other hand, this area tends
to diminish from the decrease in the thickness of the wall
of the gun in consequence of the increase in the radius of
the bore: there is consequently some value of n which will
make this area a maximum.
To determine the value of n corresponding to a maximum
area or resistance to bursting, denote this resistance by 6",
and since it is equal to the maximum bursting effort we have
from equations (2) and (4)
Regarding R' as constant and differentiating we have
7 C
Whence, placing — ^ = we find
R'= %R, or ;? = 2.
XlX. — GUN CONSTRUCTION.
That is to say, as shown by the following table, that when
R' is fixed, if the thickness of the wall is one-half the caliber,
the gun can withstand a greater bursting effort than with any
other thickness.
Table for R' = 6.
n=S R=2 S' = ^d,
n=2 R^S S" = ^ d = i S',
« = f R= 4: S'" = id= S\
It is to be noted however, that since the bursting effort for
one quadrant, or R, is equal to/„ Ry if/„ be kept constant,
-P increases with R, so that, under ordinary circumstances,
the thicker is the wall exposed to gas pressure, the greater by
Equation (4) will be the value of /^.
In order, as R increases, to diminish the value of the
radial stress, we may form the gun of two or more con-
centric cylinders. This has been done by boring out old cast-
iron guns and lining them with a tube; since, for the same
bursting effort, the pressure per unit of area on the cast-iron
is diminished because the area pressed is increased. This
will occur even if the material of the tube be of copper, the
resistance of which may be neglected, and which may there-
fore be supposed to act only by transmitting the pressure
to the outside walls.
Within limits the thicker is the tube and the greater its
value of jE, the stronger will be the composite gun, since
for a given stress on the exterior of the tube the less will
be the strain on the adjacent walls, and, therefore, the
smaller will be the maximum stress that the exterior wall
will be called upon to bear. Conversely the power of such
guns may be greatly increased. See /i, Chapter XI, p. 21.
6. From the preceding corollary it follows that if a gun,
the dimensions of which are fixed, be composed of several
XIX. — GUN CONSTRUCTION.
concentric cylinders, each one will be in the condition of
maximum strength if its internal radius is half its external
radius, or that the successive radii of contact will be in
geometrical progressio7i. This, which is known as Gadolin s
law^ is sometimes applied in modern gun construction.
EQUALIZATION OF STRAINS.
Preceding considerations show that owing to unequal
distribution of the strains in a homogeneous gun, the
strength of the gun increases much less rapidly than the
thickness of the walls.
The most favorable case would be when the whole thick-
ness of the wall was under a uniform strain, since then the
maximum pressure would be
which would be n times greater than that given by equation
(5). This result can be approximated to only by the sepa-
rate or combined application of two plans commonly known
as the methods of Varying Elasticity and of Initial Tension.
These are actually however, but variations of the former
principle.
VARYING ELASTICITY.
This consists in varying the elasticity of the concentric
cylinders as explained in Chap. XV, page 11. The elasticity
may be measured either by its coefficient or by its limit.
This divides the subject into two heads.
1. Varying Coefficient, or Rate E.
Suppose the gun to be composed of two concentric cylin-
ders, the tube containing the bore, and the jacket. If these
are of the same material the stress transmitted to the jacket
10 XTX. — GUN CONSTRUCTION.
will follow Barlow's law. But if the jacket be made of a
metal with E' > E, then the stress on its inner surface due
to the strain arising from a given increase in the external
diameter of the tube will be increased. For calling e the
common strain, /, /, the corresponding stresses, and E^ E\
the coefficients of elasticity respectively of the tube and
the jacket.
If the value of E increase as r*, then the stress on the inner
surface of the wall will he equal to that on the inner surface
of the tube.
For, let us call e^ the strain at the elastic limit of the
tube, then
8
'^ = ^
At the outside of the tube the strain will be
This will cause a stress on the inner wall of the jacket
E'e J^ E' jR^
If now E : E' :: F? : R'\ E' R^ = ER'^ and t'= d.
The thinner is the outside wall the less will the stress
vary throughout its thickness, so passing to the limit we
may say — That to develop an uniform resistance throughout a
cylinder the coefficients of elasticity of the eleme7itary concetitric
cylifiders must vary as the squares of their radii.
This principle, though frequently referred to in gun con-
struction, is now of little practical importance, since steel,
the coefficient of elasticity of which is constant, and is
XIX. — GUN CO^STRUCTION. 11
greater than that of any other cannon metal, is now gen-
erally employed for all portions of the gun.
2. Varying Limit of Elasticity.
Equation (1) shows that the stress on any cylinder is
always greatest on its inner surface, and Equation (4) that
for a given gun the value of p^ is limited by the elastic limit
of the tube.
Consequently, if the value of ^is constant, we may in-
crease the strength of the gun by increasing the elastic limit
of the tube.
This may be done in three ways.
a. By increasing the pt'ifuitive elastic limit hy varying the
composition or structure of the tube. This is not practically
done.
b. By giving it a special elastic litnit before the bore is finished,
viz. : 1st; by raising the elastic limit itself by preliminary ten-
sion, as by mandrehng (Chap. XV, p. 22), or .by firing high
proof charges. 2nd ; by lowering the origin of stresses by a
preliminary compression, as by temporarily wrapping the tube
with successive layers of wire until the surface of the bore
receives a permanent set.
c. The principle of initial tension consists in subjecting the
interior cylinders to a stress of compression by the reciprocal
extension of the outer cylinders.
The effect is to increase the work required to deform the
inner cylinders, in which the strains due to firing are the
greatest, by diminishing the work required to deform the
outer cylinders, in which the strains due to firing are the
least.
The foregoing explains the gain in strength by mandrel-
ing, and also" why the heat of firing may really tend to
strengthen a gun instead of to weaken it as is generally
VZ XIX. — GUN CONSTRUCTION.
supposed; since in both cases, the inner concentric cylinders
being expanded more than those exterior to them, stresses
are developed in the exterior cylinders which resist the further
extension of the inner portions.
It also explains the advantage of forming the tubes of more
ductile material than the jacket and hoops, since if excessive
powder pressure should expand the bore beyond its elastic
limit, the initial tension developed outside would tend to
prevent its further dilatation.
It accounts for the former preference for bronze, the duc-
tility of which sometimes caused such guns to fissure first
on the outside, where it was unsupported, while, on the
contrary, cast-iron would crack first on the surface of the
bore where the danger would less readily be seen.
Rodman's process of cooling cast-iron guns from the in-
terior by a stream of water, while the exterior of the flask
was heated by fires, was intended to utilize this principle
and was the first instance of its application on a large scale.
(Chap. XV, p. 21.)
But, while the cooling of the exterior portions of the cast-
ing might be retarded relatively to that of the portions next
to the bore, it could not be postponed until all the interior
portions had solidified.
Consequently the state of rest of such a gun could be
represented by figure 5 in which the dotted lines represent
what was desired and the full line what was attained. The
process was besides uncertain, since guns have been known
to break spontaneously from internal stresses so developed.
I APPLICATION TO BUILT UP GUNS.
The results sought by Rodman may be attained much
more certainly by the process of building up guns as ex-
plained in Chapter XV. In such a gun if the tube be com-
XIX. — GUN CONSTRUCTION. 13
pressed until, under the law by which the stresses vary, the
elastic limit of compression, p, be reached on the surface
of the bore, then the effective value of the maximum tan-
gential stress to which this surface may be safely exposed
on firing will be 6 -\- p and the maximum safe pressure for
the tube will approach as a limit
J. = iS + p)'^.
The effect of this pressure is shown in figure 6, in which
the stress will change from — p to 4- ^ on the surface of
the bore. If we take p= 6, as is commonly done, then the
stress on the exterior of the tube will change from — ^' 7\
to -^jR^ T^ as shown.
Now consider the jacket. The negative tension of the
tube is due to a positive tension of the jacket resulting from
shrinkage. Since the system is in equilibrium, the algebraic
sum of the tensions on the tube and the jacket must be equal
to 0; and, since from Barlow's law the tension, whether
positive or negative, is always numerically greatest on the
inner surface of a cylinder, we would have the condition
represented by figure 6, in which the area
RpT^R' = area R' T' T" R" .
This represents the state of the system at rest.
It is evident that the configuration of the stress area
on the jacket, and therefore the maximum stress, R' T\
which it is called on to sustain from the shrinkage, will
depend upon the thickness of the jacket. Also that R' T'
must not only not exceed the elastic limit under tension, 6' ^
of the jacket, but must be so far beneath it as to admit of
•the increment due to firing.
Now suppose the system to be placed in action by the
powder pressure and for simplicity assume that pz=: =.6',
14 XIX. — GUN CONSTRUCTION.
As the tension on the surface of the bore changes from
— pto -\- 6 the strain on the surfaces of contact will increase
the tension there by a quantity.
For the tube this will simply change the sign of the stress
from — to +.
For the jacket the addition will be positive, the most
favorable case being when the dimensions of the jacket are
so chosen, as in figure 6, that the tension at rest + the
tension in action = 6'. The state of the system in action
is shown by the dotted lines of figure 6.
The tangential resistance of the system will be propor-
tional to the sum of the areas p R B T^ R' T^ p {=%s)
+ R' T/ T,^ R" R' {= s') - R' T' T" R" R' (= s;) or
:2
:2 = 2^ + /-^, and/o= ^•
The dimensions of figure 6 render such a gun about twice
as strong as if it were a simple tube of the same size and
elasticity.
It is evident, that if, as on page 9, we suppose the gun
to consist of an indefinite number of cylinders in which the
initial tensions are properly applied, the thinner the cylinders
are made, the less will be the difference of the tensions on
their interior and exterior surfaces and the more nearly will
the broken line d T, T/ r,, become parallel to O R" , or
the more nearly will the resistance of the gun approach the
ideal case.
The difficulties of manufacture have generally limited the
number of cylinders to less than 5 but these difficulties can
be overcome by making the cylinders of continous wire
wrapped around a central tube.
XIX. — GUN CONSTRUCTION. 15
SHRINKAGE.
It is seen that the initial tension depends primarily on
the shrinkage. In built up guns this may be due to heat-
ing the exterior cylinder as described in Chap. XV, or to
forcing by hydraulic pressure one cylinder within another,
the contact surfaces being reciprocally conical, or by wind-
ing wire continuously over a central tube. By whatever
method the result may be attained, the stress on the contact
surfaces is due to the strain resulting from the compression
of the inner cylinder and the extension of the exterior.
To determine the shrinkage required to produce a given
initial compression without exceeding either p in the inner
cylinders when the system is at rest or 6 in the exterior
when the system is in action, is one of the principal objects
of the different theories of gun construction now in vogue.
A full discussion of these theories is not possible in this
course, but the following treatment of the subject based
upon Barlow's law illustrates the methods now employed.
Let e, e' be the strains on the adjacent surfaces of the
tube and jacket, for the corresponding stresses R' T^ = /,
and R' T' == /' and let o* = <? + <?' be the shrinkage strain.
/ t'
Then since e— —=^ and e' = -=r , from note, page 21,
jb JtL
<T=-^ = ^{t+n or AJi'= 5 c+o-
Consequently, as stated in Chapter XV, the tube would
be turned to a diameter
2R'
(/ + +2^'
and the jacket would be bored to its finished size. The
effect of shrinkage would be to vary the radii somewhat from
16 . XIX. — GUN CONSTRUCTION.
those assumed, and to increase the length of the tube.
These variations, which, for this discussion are not taken
into account, afford one of the best means of testing the
accuracy of the hypotheses upon which different theories of
gun construction are based.
LONGITUDINAL STRESS.
This tends to "unbreech" a gun or to produce what is
known as a "ring fracture," the plane of which approaches
that of a right section.
In homogeneous guns it was sufficiently resisted by the
sections required to resist the tangential stress; but, in com-
posite b. 1. guns, except so far as friction due to shrinkage
and powder pressure may assist, that portion which contains
the breech block has to support this stress independently of
the portions which give tangential strength.
The bursting effort is tt jR."^ p^. It tends to pull the piece
apart, generally in rear of the trunnions to which it trans-
mits the pressure causing recoil. Consequently the piece
carrying the breech block must be firmly united to the
trunnions. When b. 1, guns were first made the block was
secured to the tube, but this arrangement, although theo-
retically advantageous,* is no longer generally employed. It
is thought that the radial expansion of the tube diminishes
the bearing of the screw threads of the breech block, and
that the tube is inclined to fissure through the screw threads.
Supposing the longitudinal stress to vary through the
cross-section, its resistance may be determined as follows :
* From the analysis referred to on page 2, it follows that the longitu-
dinal stress of the tube should develop a negative radial stress which
would neutralize a portion of the powder pressure. This has been con-
firmed by experiment on a small scale, and it is said that recent cannon
made abroad have the block screwed into the tube.
XIX. — GtJN CONSTRUCTIOK. 17
The area of cross-section of an elementary cylinder whose
radius is r and the thickness of which is dr will be ^Ttrdr.
This will receive a variable stress q the intensity of which
will vary with its distance from the axis, so that the resistance
of the section whose internal and external radii are i?"and R'
q%7trdr.
n
If we suppose q to vary by Barlow's law, we have
Substituting this value of q and integrating we have for
the total resistance
^ J!L=27rie^^Nap.log— .
Equating this with the bursting effort, we have for the
condition of equilibrium
A = 2 Nap. log ^. (6)
In modern guns the ordinary values of 0, R' and R are
such that the maximum value of /^ allowed by this equation
is considerably greater than that allowed by their tangential
resistance, so that these guns are abundantly strong against
longitudinal stress.
Equation (6) is useful for computing the pressures
necessary to burst spherical shell for which purpose it gives
results closely confirmed by practice. In such cases for B
should be substituted the tenacity of the material. This is
allowable since the ductility of such castings is small.
WIRE-WOUND GUNS.
The peculiar properties of cold drawn wire described in
Chapter XV; the direction assumed by the fibers in the
gun, and the increased facility of construction have for
18 $Ct5t. — GtJN CONSTkUCtlOl^.
many years made this material a favorite subject of study
by gun makers.
Until recently, however, the difficulty of providing suffi-
cient longitudinal strength, and mechanical difficulties con-
nected with the attachment of the ends of the wires have
caused steel forgings to be preferred.
The following may be named as devices intended to pro-
vide the longitudinal resistance.
Dr. Woodbridge, of New Jersey, the originator of the
idea, proposed, after winding his tube to immerse the entire
gun in a bath of melted bronze, so as to braze or solder the
spirals and the layers together. This was found mechanic-
ally impracticable and the bath, by annealing the wire,
de&troyed much of its elasticity. Various experimenters
have tried longitudinal bars or staves connecting the trun-
nions with the breech, but so far as tried these are not
believed to have given satisfaction; the objection appearing
to consist in the difficulty of making all the bars resist
equally, for otherwise they will tend to rupture in detail.
Crozier's Wire Wound Gun.
This gun, now under construction, is devised by Lieut.
Crozier of the Ordnance Department.
It consists —
1. Of a thin steel tube forming a core for the winding;
to contain the rifling and to prevent the erosion of the wire.
It also incidentally gives longitudinal stiffness.
2. Of wire, to give tangential strength. This is preferably
of rectangular cross-section. Relying upon the support of the
wire wrapping, it is intended to produce an initial preliminary
compression considerably in excess of p. See page 11. For
experimental purposes it is assumed that the relatively thin
tube will withstand dilatation and contraction through a
considerably greater range than 6 -\- p.
XIX. — GUN CONSTRUCTION. 19
The difficulties in attaching the wires have been success-
fully overcome by electro-welding. According to the method
proposed by Mr. Longridge of England each coil of wire is
wrapped with a tension diminishing from within outwards, so
that the tension of the inner layers will be eventually less
diminished than if the tension of winding were constant.
In such a gun, properly constructed, the tangential strain
developed by firing will be uniform throughout the entire
thickness of the walls.
3. Of a steel cast jacket carrying the breech block at one
end and the trunnions at the other and so furnishing the
required longitudinal strength. It also gives longitudinal
stiffness and being lightly shrunk on it also affords some
tangential resistance. This, the heaviest unit of construc-
tion is made, of cast steel on account of its cheapness, its
radial distance and its adaptability to the present state of
the arts in the United States.
Practical Corrections.
WEIGHT OF CANNON.
The dimensiojis of cannon are sometimes increased be-
yond what is required by their elastic strength so as to in-
crease their weight and thereby diminish the destructive
energy of their recoil; because, calling E this energy, and
e that of the projectile at the muzzle, and the corresponding
masses and velocities respectively J/, ;//, ?^and v^ we have
from the equation of momenta, the general equation,
8 a m
M V =^ mv or MV=^mv or E^-^r-pe. (7)
M ^ ^
Equation (7) is an important one to remember, particu-
larly for small arms.
20 XIX. — GUN CONSTRUCTION.
This equation is not exact, since it neglects the momentum
of the powder gases, (Chapter XI, page 18), but it is con-
venient for general discussions. For a more exact formula
see Chapter XXII.
LINERS.
In order to provide against the erosion of the bore, large
built up cannon are sometimes lined for a short distance in
ifront of the chamber with a thin tube which can be replaced
with comparative facility. Guns which are properly de-
signed appear more likely to fail from this cause than as
the result of stress.
LIMITS.
It is not considered advisable to work up to the limits p
and 6 as, for the sake of illustration, has been supposed.
A safe margin is allowed in both cases. Indeed the inverse
method is that generally followed, the gun being designed
to safely resist a certain value of /<,.
It can be shown theoretically that no great advantage is
gained as to tangential strength by increasing the thickness
of the walls over the powder chamber, much beyond one
caliber. See General Remarks^ Appendix.
gadolin's law.
Owing to the practical difficulty of making perfect forgings
of the thickness which this law would require for the exterior
layers it is not generally observed.
XTX. — GUN CONSTRUCTION. 21
Note 1, Page 15.
Let R^ be the exterior radius of the tube, and R^ the interior radius of
the jacket before shrinkage ; and let R/ be their common radius after
shrinkage.
The effect of the shrinkage will be to diminish the radius of the tube
Similarly, for the jacket e' = • ^ '-^ e, since / <; /''.
The total shrinkage will be
R^-R/ R/-R,
R^ and R^ are so nearly equal to each other, and so large when compared
with the numerators of the fractions that either R' or R^ may be used
as a common denominator without material error. R' it taken because it
pertains to the tube on which the excess is left as described in Chapter XV,
The true shrinkage will therefore be slightly greater than
22 XIX. GUN CONSTRUCTION.
THE ELASTIC STRENGTH OF GUNS.
By Captain L. L. Bkuff, U. S. Ordnance Department.
The object of this discussion is to give a general idea of
the methods employed in modern gun construction, for
determining the strength of guns, the strains to which they
may be safely subjected, and the methods by which the re-
quisite strength may be obtained.
Definitions.
The elastic limit of a metal is the greatest load in lbs. per
square inch of section which the metal will sustain before it
acquires a permanent set.
There are various elastic limits, such as those for tension,
compression, torsion, etc., depending on the manner in which
the stress is applied but the only ones of practical importance
in gun construction are those for tension and compression.
The modulus of elasticity of a metal (see Michie's Mechanics,
art. 22), is the ratio of the load or stress in pounds per square
inch, to the elongation or strain per linear inch produced by
this load within the elastic limit. It is expressed by dividing
the stress by the strain. Since within the elastic limit the
strain or elongation is proportional to the stress or load, it is
evident that this ratio is constant for the same metal. Its
value for all gun steel is taken at 30,000,000 lbs.
As in the case of the elastic hmit, there are various moduli
of elasticity, as for tension, compression, etc., but those for
tension and compression, which are the only ones used, agree
so nearly, that the uniform value given above is assumed for
both.
Hooke's Law. — This law is expressed above. It is as
follows : Within the elastic hmit of a metal, the stress is pro-
portional to the strain.
Stress and Strain. — In the discussion stress will be used to
denote the force in pounds per square inch producing a given
^13^. — GUN CONSTRUCTION. 2^
extension or compression per linear inch, and strain the corres-
ponding elongation or compression produced by the stress.
General Principles.
The construction of the modern gun is supposed to be
understood. That is, that it is composed of an interior tube,
surrounded by a jacket and one or more rows of hoops.
That the jacket carries the breech-closing device, and that
the jacket and hoops have interior diameters which are less than
the exterior diameters of the parts they envelop, by a certain
prescribed amount, and that the difference in diameter between
the enveloping cylinder and the enveloped cylinder is called
the shrinkage. In order to place the smaller or enveloping
cylinders over the enveloped cylinders, the former are ex-
panded by heat till they will pass over the corresponding sur-
faces, when they are cooled in place by the application of
water.
Theory.
The principle of initial tension is employed in the modern
built up gun. The interior layers which are under the greatest
strain, due to the action of the powder gas, are compressed
by the exterior layers, jacket and hoops. When the pressure
of the gas acts upon these interior layers, it has first to over-
come this initial compression, and then to extend or compress
these layers until they reach their elastic limit for extension or-
compression, before the maximum resistance of the gun is
reached. The exterior layers are subjected to initial tension,
by which their capacity for resisting interior pressure is partly
diminished, but owing to the law of its transmission, the strain
upon them is so much less per square inch than it is upon the
interior layers that they are able to resist it. Thus the interior
layers are relieved of a portion of the strain, due to the action
of the powder gas, and the strain transmitted to the exterior
layers, by the modern process of gun construction.
24 XlX. — GUN CONSTRUCTION.
The best condition for strength in a gun is when every
layer of metal in its cross section is strained equally by a given
stress or pressure.
The foundation of the theory of the built up gun is
this. That ifi whatever state the gun may be considered^
whether under the pressure of the powder gas, or free from it,
7ione of the fibers of any cylinder in the gim shall be elongated
or contracted beyond the elastic lifnit of the metal of that
cylinder^ which elastic limit is determined by the test of the
metal in a testing machine.
Two states or conditions of the gun are considered in this
discussion ; one, called " the system in action," which means
that the gun is subjected to the maximum interior pressure
which it can support with safety, and the other, called " the
system at rest," that is, when the gun is free from the pressure
of the powder gas, although the strains due to the shrinkages
still exist.
Methods of Discussion.
The general method of discussion is :
First. To assume a cube of metal the length of whose
edges is unity, and which is supposed to be perfectly elastic
up to a given limit ; to deduce the equations of equilibrium
which show the relations between the forces acting upon this
cube in directions at right angles to its faces, and the corres-
ponding elongations and contractions produced by them.
Second. To transform these equations so that they will apply
to the elements of a cylinder of metal ; or in other words, to
deduce the equations which give the relations between the
stresses at different points throughout the right section of a
single cylinder.
Third. To pass from a single cyhnder to a compound
cylinder composed of any number of single cylinders, and to
deduce for the latter the compressions and extensions pro-
XIX.— GUN CONSTRUCTION. 25
duced by given pressures, and the shrinkages or differences
of diameter which will produce given compressions and
pressures.
FIRST. — EQUATIONS OF EQUILIBRIUM FOR A CUBE OF METAL
OF CONSTANT ELASTICITY WHOSE EDGES ARE EQUAL TO
UNITY.
It has been found by experiment, that when a cubical elastic
solid is acted upon by a given force of extension or com-
pression in a direction perpendicular to two of its opposite
faces, this force produces an extension or a compression of
the cube in the direction of the force, of a given amount, and
a corresponding compression or extension in the two direc-
tions at right angles to the given force equal to one-third
the first extension or compression.
The force is supposed to be within the elastic Umit of the
solid.
For example, suppose a force of extension /*, Fig. 7, to act
upon the opposite faces of a cube of metal, whose edges are
each one inch long. If it extends the edges a a a ^^ of a.n
inch it will shorten the edges d I? d and c c c ^ of ^^ :=: ^ oi
an inch, and the same for any other force.
In figure 8
Let B = the modulus of elasticity of the cube.
X, V and Z= three forces acting at right angles to the
faces of the cube, being tensions in the figure.
X; fi; V, =z the extensions produced by the three forces
Xy Fand Z, respectively.
Then the force X, according to the preceding principle,
produces an elongation in its own direction equal to
But the force K diminishes this elongation by the amount
iZ
26 XIX — GUN CONSTRUCTION.
and the force Z by the amount
Hence the total elongation in the direction of X is
In the same way we have for the total elongations in the
directions of Kand Z
'=4{-f-^)
These three equations express the relations between the
elongations of the faces of an elastic cube whose edges are
unity, and the corresponding forces acting on them.
SECOND. APPLICATION TO AN ELASTIC CYLINDER.
We have supposed the three forces to be tensions. In the
case of a gun cylinder, however^ two of the forces are ten-
sions, one acting in the direction of a tangent to the cylinder,
and the other parallel to the axis, while the third is a pressure
and acts in the direction of the radius. In Figure 9, let / =
the radial pressure, / = the tangential tension, ^ the longitu-
dinal tension, per unit of area.
Substitute / for X, — J> for Y since it acts opposite to F,
and ^ for Z, and the above equations become
}
'--M' + T + l)) W
XIX. — GUN CONSTRUCTION. 27
The first of these equations expresses the total change per
unit of length in the direction of the tangent of the cyhnder ;
the second the total compression (being negative) in the
direction of the radius ; and the third the total change in the
direction of the axis, due to the three forces /, / and q.
In order to apply these equations in practice the changes of
dimensions must be expressed in terms of the radii of the
cylinder and of the forces acting upon it. To express the
equations in these terms we proceed as follows :
Equations of Equilibrium in Terms of the Radii of the
Cylinder.
Let Figure 10 represent a section of the cylinder perpen-
dicular to the axis.
Let R = interior radius.
R ' n: exterior radius.
r = the radius of any circle of the section.
r' = any other radius exterior to r.
p zzzthe radial pressure per unit of surface at the distance
r from the axis.
tz=. the tangential stress per unit of surface at r,
q = the stress per unit of section parallel to the axis of
the cylinder, and supposed uniform throughout the
section.
/*=the interior radial pressure per unit of surface,
being the value of / for R.
^'^the exterior radial pressure per unit of surface,
being the value of / for R' .
T and T' = the values of / for r = Rj and r= i?' re-
spectively.
^=the modulus of elasticity.
The pressure/, whether acting inward or outward, develops
in the direction perpendicular to A B, Figure 10, a force
equal to 2j>r.
28 XIX. — GUN CONSTRUCTION.
Increase r to r', and represent by f the new value of/.
This develops a force in the direction perpendicular \.q A B
equal to 2 p' r* . The algebraic difference between these forces
is in equilibrio with the product of twice the thickness of the
ring r* — ;' into the mean stress throughout the ring, which
represent by r. Hence
2/ / _ 2 /r = — 2 T (^ — r)
dividing
P'r' —pr _ ^
r* — r
passing to the limit of the ratio in the first member by making
d{pf)
( p' r' —pr \
limit of 1 , ^
r' ^
limit of
\>
Hence
d (pr) __
Taking the last of Equations (8), which expresses the strain
in the direction of the axis of the cylinder, and supposing
this uniform throughout the cross-section, we have
P\
^=M'
i+8
From this we have
or t— p=^^{q— V E) (10)
But the second member of this last equation is constant,
since we have supposed v uniform throughout the section ;
hence
/ — / = constant.
XIX. GUN CONSTRUCTION. 29
From which we may unite
t—p= T—P (A)
t—p=T' — F' (V)
From Equation (10) we have
t=P + i(q-vE) (11)
Substituting this for / in Equation (9) we have
performing the differentiation as indicated ; / and r being
variable,
pdr + rdp ^ o / Z7\
Jr = — / — 3(^— v^)
reducing
dr dp
r ~~ 2 / + 3 (^ — V ^)
Integrating
log= (y) = 4 log. (2/ H- 3 (? - V ^ + log. C
i- = ^(2/ + 3(?-r^))
Substituting the value of/ + 3 (? — v E) from (11) we have
! = .(/+/)
(/ -j- /) r' = — = constant
From which we can write
{t^- p)r' = {T-^P)R' (Q
{t-\- p)r' = {T' -\-P<)R''' {D)
From Equations (A) and (B) we derive the following
principle :
The difference between the tension and the 'Pressure is the
same at all points.
30 XIX. — GUN CONSTRUCTION.
From (C) and {D) we have the following principle :
At any point whatever^ the sum of the tension in the direction
of the circumference, ajid of the pressure in the direction of
the radius, varies inversely as the square of the radius.
This demonstration is given by Captain Crozier, Ordnance
Department, in " Notes on the Construction of Ordnance,"
No. 35.
Applications. — It has been shown by Captain Birnie, Ord-
nance Department, that in considering the radial and tangential
strains in a gun cylinder, we may, without appreciable error,
omit the longitudinal strain, or the strain parallel to the axis,
and afterwards consider this latter strain separately. This
conclusion has been proved to be correct, by actual measure-
ments of guns during construction. This is equivalent to
making in Equation (8)
q^o,
when the equations become
In the last equation, which gives the change in the longi-
tudinal direction, this change will be produced by/ and /only.
From Equations (C) and {D) we have
(5-/ -j- pi) Ri 2 ^ (r-l. p) j^^
and from {A) and {B)
T' — F' = T—F
Combining these two equations and ehminating T' we
have
■ F'^ + J^ 2 F' ' F'
^ ^' F'^ — F*" F" — F"
/ =
XI3^. — GUN CONSTRUCTION. 31
Substituting this value in (J) and (C), combining the re-
sulting equations, and eliminating/ we have
Ri^ — R' -I- ^,2_^. ^ (13)
And by combining and eHminating / between the same
equations we have.
_ FJ ^ — P' Ii'\ . J^'^^'iP—P') 1
Substituting these values of / and / in Equations (12) we
have
2 {PR' — P' R'^) q^R'^ R' i^P— P') 1
'^ "" $(R" — R')jS "f" 3{R'' — R')£ r" ^^^
_ ^(PR"— P' R'"") 4tR" R' {P—P') 1_
^— d(R'^ — R')£ ~" S {R' ' — R') E r" (^^^
_ ^{PR' — P'R'')
^ — "" 8 (i?"* — R') E vA ')
These equations give the values of the elongations or con-
tractions in terms of the pressures and radii, and the known
modulus E^ for any radius r.
Elastic Strength of a Simple or Single Cylinder.
Now it may be shown that the greatest elongations and
compressions of the fibres of a cyUnder subjected to an interior
pressure P, and an exterior pressure P' , take place at the inner
surface of the cylinder. (See appendix, Note 35, on the Con-
struction of Ordnance.) Assuming this, we recur now to the
fundamental principle stated above "that no fibre of any
cylinder in the gun shall be elongated or contracted beyond
the elastic limit of the metal of that cylinder."
Let Q = the elastic limit for tension,
p = the elastic limit for compression in pounds or tons
per square inch, of the cylinder.
82 XlX. — GUN CONSTRUCTION.
Then the extension and compression at the elastic Hmit will
be respectively
and by the above principle these must be equal to the greatest
values of /I and [z respectively.
Since the greatest extensions and compressions will occur
at the interior of the cylinder, we have for their greatest
values by substituting jR for r in (15) and (16)
3 (i?' ' — R') E
(18)
f^ — — 3 (i?' » — R'YE (^^)
Placing these equal to -^ and -^ respectively, we have
. (4:R" + 2R')P—6R" P'
d(R'' — R')
I 2 pt
___ (^R'^ — 2R')P—'2R'''P
P— 3(R'' — R')
From which we find two values for P, viz. :
■^ 4 i?' ^ + 2 ^^
^ — 4: R" — '2.R'
(20)
(21)
Equation (20) gives the value for the interior pressure,
which will cause the layer of metal on the interior of the
cylinder to reach its elastic limit by extension, and Equation
(21) the value which will cause the same layer to be com-
pressed to its elastic limit ; these pressures being in pounds
or tons per square inch according as d and p are expressed in
pounds or tons.
XIX. — GUN CONSTRUCTION. 83
It must be remembered that the less of the two pressures,
measures the elastic strength of the cyHnder.
THIRD. — THE ELASTIC STRENGTH OF A COMPOUND CYLINDER,
OR OF A BUILT-UP GUN.
For the sake of clearness in the nomenclature, and of sim-
plicity in discussion, the gun will be supposed to consist of two
cylinders only, shrunk one upon the other, and the resistance
of this compound cylinder, and the shrinkages to be used in
its construction, will be deduced.
In figure 11 let
P^ = the maximum internal pressure to which the
gun can be subjected.
P^ ■=. the normal pressure at the surface of contact
of the two cylinders.
P^ •=. the exterior normal pressure.
A' Pv P-i ^^ variations in the pressures, P^^ P^ and P^ due
to any cause whatever.
The above pressures and variations of pressure are those
which exist with the " system in action," — that is when the
maximum gas pressure is acting on the bore.
Let
PI = the normal pressure acting at the surface of
contact of the two cylinders when the system
is at rest — that is, when the pressure of the
gas does not act on the bore.
// = the variation of P^ due to any cause whatever.
J?g, i?j, R^ = the radii of bore, of interior of second cylinder,
and of exterior of second cylinder respectively.
0„, 0j =: elastic limits of inner and outer cylinders for
extension.
p^, pj = elastic limit of same for compression.
E^, E^ = moduli of elasticity of metal of cylinders.
34 XIX. — GUN CONSTRUCTION.
Writing Equations (20) and (21) we have
^ - 4^'^ + 2i?^~ ^^
^ — 4^'" — 2i?^ ^^^
Now it will be remembered that in the case of a single
cylinder, Equation (20) gives the value of Z*^^^, the interior
pressure which will cause the layer of metal on the interior
of the cylinder to reach its elastic limit by extension, and
Equation (21) the value of P^^ the interior pressure which
will cause the same layer to be compressed to its elastic limit.
Taking the outer or second cylinder of the gun, it is always
under a strain of extension both in action and at rest, and
hence Equation (21) will not apply to it.
Equation (20) must therefore be used. To apply it to the
present case, R and R' in (20) are the inner and outer radii,
which now become R^ and R^ respectively. /*is the interior
pressure, and it now becomes P^, P' is the exterior pressure,
and it becomes P^. But this exterior pressure on the second
cylinder is simply that due to the atmosphere, and it is so
small in comparison with the other pressures considered that
it may be neglected. Hence
P. — o.
Also Q becomes Q^. Making these substitutions in (20) we
have
_ %{R^-R^)Q,
' ~ 4: Rl + 2 R,'
This gives the value of the interior pressure on the outer
cylinder which will cause its inner layer to be strained to the
elastic limit for tension, and as this value is expressed in
XIX. — GUN CONSTRUCTION. 85
known terms, P^ can be readily calculated. The value of 0^
is obtained from test of the metal in a testing machine.
Now taking the inner cylinder, the pressure P^ just found, acts
not only on the interior of the outer cylinder, but also on the
exterior of this inner cylinder. Hence one of the normal
pressures acting on this inner cylinder is known, and we have
to calculate the other. •
This inner cylinder is not only extended by the action of
the powder gas, but it is also compressed radially by this
pressure, and it is subjected to a strain of compression by the
force P^ which we have just found. In other words the inner
cylinder is subjected to both tension and compression, and
hence it is necessary to calculate both strains, and to take the
smaller as the limit of its elastic resistance.
Referring to Equations (20) and (21) the following changes
must be made to apply them to the inner cylinder —
P becomes P^
P' " P^
R " R,
R' '* R^
e - 6^
Making these substitutions we can write
,, 3{R,^-Rl) e,+ 6R,-'P,
V 4:R,' + 2 Rl
» ~ 4:R,^ ^2Rl
Substituting in these equations the known values of the
radii, and of ^^ and p^ together with the value of P, just cal-
culated, we obtain two values for /*„, the smaller of which is
the limiting value of the pressure for the compound cylinder
under discussion.
86 XIX. — GUN CONSTRUCTION.
For convenience of reference these equations are collected
here —
p ^ 3 (i?i - R,' ) e,
4 7?^ + 2 R,'
^ (n _ 3(^.'-^a K^ ^^.'P. V (22)
•^o ~ 4i?,^ + 2J?,1 ^ ^ ^
3 {R, - i?^) p„ + 2 i?,' -P.
p(2) _
The values of P, obtained from Equations (22), are the
pressures which will cause the interior of each cylinder to
reach its elastic limit for extension or compression; and since
the greatest strains in a cyHnder occur at its interior surface,
and since also no part of any cylinder must be strained be-
yond its elastic limit, it is evident that the values of P, thus
obtained, represent the greatest strains to which the cylinders
can be subjected. It will be seen hereafter, that these values
cannot always be used in practice, since the bore in the state
of rest, may be compressed beyond its elastic limit, by the use
of these values.
It is, therefore, necessary now to consider
The System at Rest.
Equations (22) give the pressures acting for the sys-
tem when under the maximum pressure of the powder
gas. It is evident, however, that when the system is at
rest, great pressures will exist at the surface of contact of
the two cylinders, due to the shrinkage of one on the other.
These pressures generally increase from the exterior to the in-
terior, and the interior of the bore is generally compressed
from this cause to a greater degree than any other part of the
gun. This compression of the bore may be so great as to
exceed the elastic limit for compression of the metal of the
inner cyHnder, and thus, although the gun is properly calcu-
lated for action, the principle upon which the whole structure
XIX. — GUN CONSTRUCTION. 37
is built may be violated, when the gas pressure is removed.
In this case", the elasticity of the tube is destroyed., as effect-
ively as if by the powder pressure.
It is evident, also, that when the powder pressure ceases,
the pressure which existed at the surface of contact of the two
cyhnders will change, and will assume some other value for
the state of rest. The value of this variation of pressure at
the surface of contact has been denoted by /, and at the sur-
face of the bore by /o- The value of the pressure at the sur-
face of contact for the state of rest has been represented
by P\
Now it is evident that the difference between the pressure
in action and at rest for any surface, gives the variation in the
pressure at that surface. Hence, since the pressure at the in-
terior of the bore, when the system is at rest, is zero, we have
and also
When these changes of pressure occur, they are accompanied
by corresponding changes of dimensions of the surfaces at
which they act, and these changes of dimensions depend
directly upon the variations of pressure. The greatest changes
of dimensions occur in the direction of the circumference or
of the tangent to the surfaces, and Equation (18) gives the
value of these changes for the interior surfaces.
To Calculate these Changes of Dimensions.
The variation of pressure acting on the outer cylinder .s
/,, and the exterior pressure is zero, being that of tlie atmos-
phere. Hence, substituting in Equation (18) for P its value
p^ and making
/" = o
R -^ R,
R' ^ R,
E =^ E,
38 XIX. — GUN CONSTRUCTION.
we can write
^^(4^^ + 2i?r)A
3 (J^l — R:^) E,
This represents the change of dimensions of the interior
of the outer cyUnder per unit of length of circumference,
under the change of pressure represented by p^.
To find the change of the exterior of the tube due to the
variations of pressures p^ and /, which act on it, we recur to
the general Equation (15), which gives the change in the
direction of the circumference, or of the tangent, of any
cylinder whose exterior and interior radii are R' and R at the
distance r from the axis. Replacing r by R' since the change
at the exterior of the cyHnder is now required, we have
_ %R^P-{^R^ + ^R'^)P'
^ - 'i{R''^-R^)E ^^^^
To apply this to the inner cylinder now under discussion
make
R' = Ry
and we write
6 Rl A. - (4 Rl + 2 R,') A .
A-=
3 {R,^ - Rf) E,
for the value of the change of exterior of inner cylinder or
tube.
Now since the outer surface of the tube, and the inner
surface of the outer cylinder are in contact, the same change
of dimensions must occur in both, at this surface of contact,
and hence the two values of X obtained above are equal.
XIX. — GUN CONSTRUCTION. 89
We have therefore
6 RIP, — (4 i?^ + 2 R^)p, (4 i?l + 2 R^) /,
/i =
Solving this equation with reference to p, we have
QR,E,[Ri-R,']p^
E, {R,—Rn (4i^o + ^Rn + E,(J^,^ — J^t) (4^^ + 2 R,')
(24)
Now in this equation /„ is known, since it is equal to — P^
as before shown, and R^ has been already calculated by-
Equations (22), hence we can calculate/,.
Limiting Value for the Exterior Pressure on the Inner Cyl-
inder, System at Rest.
It has been stated that R^, given by Equations (22) represents
the maximum stress to which the gun can be subjected in
action, the smaller of the two values of P^ being used. It is
necessary now to determine what value can be allowed for
the exterior pressure upon the inner cylinder at rest, so that
the interior surface of the latter will not be compressed by it
beyond its elastic hmit. To do this we must find the value
of Ri for the state of rest.
The value of R/ for this state is as has been shown
R/ =R. + Pi
Assuming Equation (18) and making P — o^ since the
interior pressure at rest is zero, we have
~2 R"" P'
A —
{R^ — P')E
which shows since it is negative, that there is tangential com-
pression, and as this is generally greater than the radial com-
pression. Equation (18) only is used.
This compression must not exceed that at the elastic hmit
40 XIX. — GUN CONSTRUCTION.
which is
P
E
hence we have
for the limiting value of the compression at the interior of the
inner cylinder. Changing the letters to correspond to the
case of the tube under discussion ; that is, making
F' = P/
R' ^ R,
R ^ R,
E ^E,
P = Po
and omitting the negative sign, as that simply indicates com-
pression, we write
2 R,' r/ p.
or
but
hence
(y?.' - K) E^ E,
^, ^ (i?,' - F?^ p.
2/C
^ = ^. + A
/>/=/». + /. ^ ^^-'^"5^° (25)
and this value of P^ must not be exceeded.
This equation gives the value of /*/ r= P^ -(" A i^^ known
terms.
But we have the value of /i from Equation (24) by substi-
tuting for /„ its value — P^. Hence, substituting the value
of /i from Equation (24) in (25), we obtain a new value for
P^ which will cause the interior of the inner cylinder to be
compressed to its elastic limit at rest. The value thus ob-
XIX. — aUN CONStRUCTlOl^. 41
tained for P^ must be substituted in that one of Equations
(22) which gives the least value for P^. The new value thus
obtained for P^ will be such that the inner cylinder will not
be strained beyond its elastic Hmit either in action or at rest,
and it represents the greatest value of the stress to which the
gun can be subjected without exceeding the elastic limit of
the metal composing it.
THE SHRINKAGE.
In Fig. 12, let OA represent the interior, and OB the ex-
terior radius of the inner cylinder, and OC and OD the inte-
rior and exterior radii of the outer cylinder, before they are
assembled to form the gun. Then the length CJS= OB — OC
is the shrinkage. As diameters are usually employed instead
of radii in tables of shrinkages, a more usual expression for
the shrinkage is
2 C^ = 2 {OB — OC)
or, in other words, the shrinkage is the difference of diameters
of the enveloping and enveloped cylinders. This is called
the absolute or actual shrinkage. The relative shrinkage is
the shrinkage per unit of diameter, or per unit of radius, and
is expressed by dividing the absolute shrinkage by the interior
diameter of the outer or enveloping cyUnder. Thus the rela-
tive shrinkage in this case is
2CB ^ '^(OB— OC) CB
^0C~ 2 0C ~ OC
To determine the shrinkage for the case under discussion. In
Fig. 12, let OA, OB, OC and OD represent the same quan-
tities as above.
Now, when the outer cylinder is heated and expanded till
its interior radius OC is slightly greater than the exterior ra-
dius OB of the inner cylinder, and the exterior cylinder while
hot is placed on the interior cylinder, so as to envelop it, and
4^ XIX. — GUN CONSTRUCTlOM.
is then cooled in this position, it is evident that the outer cyl-
inder will compress the exterior of the inner one, and that
their surface of contact will assume some such position as
K E E''y the outer radius O B oi the tube being compressed
to O E^ and the inner radius O C oi the outer cylinder being
extended to O E, Hence the radius O B has been compressed
by the amount
OB — OE z= BE
and the radius OC has been extended by
OE— 0C=^ CE '
and the sum of these two is equal to the original shrinkage,
BC, or
BE -^ CE^ BC,
Hence, if we can find the values of the two quantities BE
and CE^ we will have that of the shrinkage.
Now when the two cylinders are assembled, and the system
is at rest, we have found that the pressure P^ acts at the con-
tact surface of the cylinders. That is, the exterior cylinder is
acted upon by a force represented by P^, and this force pro-
duces an extension per unit of radius of
CE
OC
CE being unknown. But Equation (18) gives the value of
this extension in terms of the radii, pressures and modulus of
the cylinder. Remembering that
P' = P^ — o
P =P,'
R' = R,
R = R,
E =E,
we write
CE _ (4 ^^ + 2 R,') P!
OC ~ 3 {Rl ~ R^')E,
This gives CE,
XIX. GUN CONSTRUCTION. 43
To find BEy or the compression of the exterior of the tube.
The pressure acting is P/, as before, the interior pressure
being zero. This change being at the exterior of the cyHnder,
we use Equation (23), making the following changes,
P = o
P' = P^
Hence we have
E =E,
oc ~ ■^ -
(4 iP„ + 2 J?,') P!
- 3 {R;- - Rl) E,
Strictly speaking, the true value is -—- for the change per
unit of radius, but the difference between OB and OC '\s so
small in practice that either may be used without appreciable
error.
Now it will be observed that the value of -^ = A just ob-
tained, is negative, indicating compression, and this is evi-
dently correct.
But the shrinkage sought is the sum of two positive quan-
tities
BE 4- CE CB
'OC ~ ~0C
In order to avoid the negative sign, and obtain the quantity
BE
j^ under a positive form, we suppose that the exterior cyl-
inder is removed from the interior cylinder. In this case it
is evident that the exterior surface of the inner cylinder will
expand and regain its original diameter, and that this expan-
sion is exactly the same in amount as the compression BE,
which was produced by shrinking on the outer cylinder.
This is equivalent to supposing the pressure P^' neutralized
44 XIX. — GUN CONSTRUCTION-.
by an equal and opposite pressure ; that is, in the value of
BE
--T. we make
P.' = - A'
and that value becomes accordingly —
BE _ (4 R^ + 2 R^) F,'
a positive quantity. Now denoting by op the shrinkage of
the two cylinders, we have
CE-\.BE (4^/ + 2i?.^)P/ (4.R:-^<2R,^)P'
^ OC ~ ^ (R^' — R:') E,~^S (R,' — R^') E^ ^ ^
In using this equation it must be remembered that cp is the
relative shrinkage, or the shrinkage per unit of diameter. To
obtain the absolute shrinkage, the relative shrinkage must be
multiplied by the diameter. That is, if Z> represent the diam-
eter and (p the relative shrinkage (both in inches), and *S the
absolute shrinkage, then,
S ^ (j)X z>
and the exterior diameter of the cylinder must be made
E>' = D-{- S
Referring to figure 12,
2 OC^ jD
2CR=S=q)XZ>
2 0B= D'
GENERAL REMARKS.
It can be shown theoretically that the maximum resistance
is obtained from a gun cylinder when the radii of the differ-
ent cylinders composing it, vary from the interior in geomet-
rical progression.
XIX. — GUN CONSTRUCTION.
45
This, however, is never adopted in practice for various
reasons, one of the principal being the objection to very thick
cylinders on account of their being more difficult to forge,
less uniform in quality, and more liable to imperfections in
the metal.
It can also be shown that no great advantage is gained as
regards tangential strength, by increasing the thickness of the
walls of the gun over the powder chamber much beyond one
caliber. These considerations combined with the capacity of
the forging plant where hoops, tubes and jackets are made,
will serve to fix the limits of thickness of the different cylin-
ders composing the gun. Examples are given here of three
modern guns :
Gun.
Diam. of
powder
chamber.
Thick-
ness of
tube.
Thick-
ness of
jacket.
Thick-
ness of
-Whoops.
Thick-
ness of
£ hoops.
Total
thickness
of wall.
Total
thickness
of wall.
Inches.
Inches.
Inches.
Inches.
Inches.
Inches.
Calibers.
8-in.
9.50
2.75
4.25
3.30
10.30
1.0842
10-in.
11.80
3.20
4.90
2.525
3.10
13.725
1.1631
12-in.
14.20
3.90
5.80
2.90
3.425
16.025
1.1285
The caliber being the diameter of the powder chamber,
the above table shows that the thickness of wall only sHghtly
exceeds one calibre.
Having determined from the above considerations the
radii of the different cylinders composing the gun, the values
of the pressures which the gun will support in action may
be calculated from Equations (22), B and p being known
from tests of the metal in a testing machine.
Having obtained the values of /{ and F^ from Equations
(22), the system must be considered at rest, and the values
of the pressure P/ deduced which will be safe for that state
of the system. This is given by Equation (25).
Then this value of P^' must be used to deduce a new
46 XIX. — GUN CONSTRUCTION.
value of Z*! , and this value of P^ must be substituted in that
one of Equations (22) which gave the lower value for P^ .
The new value of P^ thus deduced will represent the maxi-
mum pressure to which the gun can be safely subjected.
We can now calculate the shrinkage from Equation (26),
using the value of P/ already found.
The same method can be extended to guns composed of
any number of cylinders, but the subject becomes more
complex as the number of cyhnders increases.
After calculating the shrinkages, the same fundamental
formulas may be used to calculate the compressions of the
bore produced by the assembhng of the cylinders. The
results of these calculations are then compared with actual
measurements of the bore made during the assembling of the
gun, and the agreement is in every case found to be
remarkably close, and furnishes a proof of the correctness
of the theory.
Thickness of Gun at Different Points.
The thickness of the gun at the reinforce is determined by
the considerations already given, and as stated, rarely
exceeds one and a half calibres. To determine its thickness
at various points along the chase, it is necessary to have the
'* pressure curve " of the powder at different points along the
bore. Formulas have been deduced for this curve by various
authors, but it is not deemed necessary to give them here.
The results obtained from them do not agree, and recent
experiments on a small gun show that Noble & Abel's formula,
Chapter IX, agrees very well with the results of experiment.
Using this formula, the pressure curve can be obtained.
The elastic resistance of the gun, or the values of P^ for
different sections of the gun, are calculated as explamed, and
plotted, and the curve of powder pressure for the same gun
XIX.— GUN CONSTRUCTION. 47
is also plotted to the same scale. The curve of resistance
should always He above the curve of pressures.
Length of Gun.
This may be determined for a given initial velocity and
given conditions of loading, charge of powder, etc., by
Sarrau's formulas for velocity, but as a practical rule, it may
be stated that at present the total length of modern high
power guns varies between 35 and 45 calibres, and that the
tendency is toward the higher limit.
XX. — EXTERIOR BALLISTICS.
CHAPTER XX.
EXTERIOR BALLISTICS.
This treats of the motion of the projectile after it has
left the gun.
Definitions.
The sights are two projections on the upper surface of
the piece, the distance between which parallel to the axis,
is called the sight radius^ or sometimes the radius of the
gun.
Each sight contains a definite point called the sight point.
That for the front sight, which is fixed, is generally deter-
mined by the intersection, at an acute angle, of the faces
of a wedge or by the intersection of cross wires as in sur-
veying instruments. That for the rear sight consists of a
notch in a bar, or a pin hole.
The rear sight point is movable so as to vary its distance
from the axis.
The difference of the distances of the sight points from
the axis of the bore, divided by the radius of the gun, meas-
ures the tangent of the angle of elevation^ or of <f, figure I.
The line of sight is a straight line passing through the two
sight points. In the act of aiming it also pierces the target.
In this case, therefore, the angle of elevation is the angle
included between the line of sight and the axis of the bore.
The line of departure is the line in which the projectile is
moving when it leaves the gun. It is therefore the tangent
to the trajectory at the muzzle. Owing to the incipient
recoil, due to the conservatism of the system (Chapters VII,
XX. — EXTERIOR BALLISTICS.
XXI), and to necessary looseness of the joints between the
trunnions and the carriage, and between the carriage and the
wheels, the piece tends to revolve slightly about some point
in rear, so that the projectile does not always leave the piece
in the original direction of the axis. The angle included
between the axis and the line of departure is called the angle
oi ju7np,j\ figure 1. If to attain a given target the jump,
which is almost always positive, were neglected, we would
find d'> q and the computed value of e would be too great,
so that the target would be overshot.
The angle made by the line of departure with the horizon-
tal plane is called the angle of departure, d, figure 1. It is
with this angle that we have principally to deal in ballistics,
as it is the angle at which the projectile actually begins its
flight.
The angle of projection is the angle included between the
line of departure and the line of sight ; it may be thought of
as the angle of elevation corrected for jump.
The quadrant angle is the angle made by the axis of the
bore and the horizontal. It is measured by the gunner's
quadrant, a form of spirit level, applied to the face of the
muzzle or to some cylindrical surface of the gun. Owing to
the grooves in rifled guns this is preferably an exterior surface.
See q, figure 1.
The quadrant angle may be measured either above or
below the horizontal plane. The term depressed or plunging
fire refers to a negative quadrant angle.
The angle of sight is the angle included between the line
of sight and the horizontal plane, or s^ figure 1.*
* This depends solely upon the altitude of the target in the astronomi-
cal sense. It is unfortunate that the term above named should be used
to designate this angle, as it has nothing whatever to do with the sights.
It would be more consistent if the terms angle of sights and of elevation
were exchanged. In the P>ench service the angle of sight is called the
angle of site.
XX. — EXTERIOR BALLISTICS.
It is seen from the figure and by definition that
Of these quantities, s is given by the act of pointing, and
e must be computed by the methods hereafter explained.
The above equation is principally useful for verifying the
elevation given by the sights or for guns which are not pro-
vided with sights.
To determine the Jump,
Place in front of the gun and at a distance just beyond
the reach of the blast a slight screen. Mark upon the screen
the point o^ at which it is pierced by the axis of the bore
prolonged. In breech-loaders this may be done by means
of perforated discs fitting the bore, and in muzzle-loaders
by making ^ = and laying off on the screen the coordi-
nates of the sight points negatively taken.
Fire the piece and determine V.
If then X and y are the horizontal and vertical coordi-
nates of the center of the shot hole when referred to ^, and
d the distance of the screen from the muzzle we have
approximately, from figure 2,
tan J —
._y -Vab
d
^t^ d
but ad= ^ and t= ~ neartyj
hence tan /= | + ^^.
If the shot strikes below the point, then y is measured
negatively.
X
The lateral jump is evidently tan~^ = —,
" Cti
XX. — EXTERIOR BALLISTICS.
A number of such determinations should be made since
the method is obviously inaccurate.
A better plan is to eliminate the effect of the perturba-
tions near the muzzle by computing e and determining by
experiment the value of p for an extended range of, say
600 yards, — then j — p — e
The jump is usually about 30' which value will be taken
in problems in which it is required to be assumed.
The planes of sight and of departure are vertical planes
containing the corresponding lines.
The computed range is the distance from the gun to the
(second) intersection of the trajectory by the line of sight.
The term range is also applied according to circumstances
to the distance of the target from the gun, and to the hori-
zontal distance to the point of impact — in case the target
be missed and the projectile strikes some horizontal surface
in front or rear of the target — such as water.
Practically the dimensions of the gun may be neglected
so that the front sight point may be considered in the axis
of the bore and the range to be measured from either sight
indifferently.
In the following discussions we will also assume that the
planes of sight and of departure coincide in the vertical
plane containing the axis of the piece, which is called the
plane of fire^ and that the projectile travels in the plane
of departure.
This is not actually true, however, for the projectile tends
to move sideways out of the plane of departure as shown by
the horizontal projection of figure 1. This motion, called
the drifts is due to the combined effect of the rotation of the
projectile and the resistance of the air ; combined with other
causes of inaccuracy it leads at the target to lateral deviation^
which is meaured by the distance of the point of impact from
the plane of sight. See Chapter XXX.
XX. EXTERIOR BALLISTICS.
The deviation in ran^e is similarly measured.
Classification of Fire,
In this classification the sights are disregarded and the
line of fire is the straight line from the muzzle of the piece
to the point aimed at. Similarly for general discussions the
quadrant angle is sometimes called the angle of fire.
Figure 3 illustrates the classification with reference to
the vertical plane containing the target, which represents a
certain face of a work.
Figure 4 illustrates the classification with reference to
the horizontal plane. The limit for direct fire is imposed
by the principle of the rigidity of the trajectory to be here-
after explained.
The classification is also applied, as indicated, to the
angles of descent. This is more accurate since it relates to
the effect produced rather than to the intention of produc-
ing a given effect.
In figure 1 it is assumed without sensible error, that the lines of
sight, departure, etc., intersect at the muzzle, and the drift is very much
exaggerated.
XX. — EXTERIOR BALLISTICS.
Exterior ballistics is usually divided into tw© parts. 1st,
in vacuo; 2d, in the air.
I TRAJECTORY IN VACUO.
Utility.
The first of these is sufficiently treated in the course of
Mechanics. Its practical utility is confined to two cases.
1st. That of projectiles of high sectional density moving
with comparatively low velocity as in mortars, since in such
cases the loss of energy due to the resistance of the air may
be neglected where only approximate results are required.
Chapter XVI, page 1.
2d. Cases involving the flight of projectiles in the air, in
which some of the data are lacking, or in which the velocity
of the projectile in one of its component directions is so
low that the consequent retardation may be neglected.
» USEFUL FORMULAE.
The principal equations of this kind which are used in
this course may be derived from equation (167), Michie,
in which we write, as is customary, y for z,
^ = Vsme-st; (1)
whence
j= Vt sin d- ^r^ (2)
and by placing -^ =0
(3)
for the time to the vertex of the trajectory.
XX. — EXTERIOR BALLISTICS.
From the symmetry of the trajectory in vacuo, T, the
whole time of flight is equal to 2/ or
and
Eliminating V by substituting this value in Equation (2),
y^q.(T-i) (6)
T s: T^
If in this we replace /by — we have F= ^—5 — (7)
in which jj' now becomes F, the ordinate of the vertex.
That is, the height of the vertex in feet is nearly four
times the square of the time of flight in seconds.
Equations (6) and (7) are important, and should be re-
membered, as they are frequently used in approximate solu-
tions in the air.
If in Equation (169), Michie, rewritten according to the
usual nomenclature, or
y = X tan — -r--- ^-^ (8)
in which ^is the height through which the projectile must
fall to acquire the velocity F, we make j = 6 wq may
determine the range X
2 V sin cos (9 _ V sin 2 d
X =: (y)
g g
Therefore the range will vary less from variations in 0, as
d approaches 45°.
Also, for the same value of B, as in S. B. mortars,
X: X' -.'.V^: V'\
XX.— EXTERIOR BALLISTICS.
But, considering the powder as a reservoir of potential
energy, frona the equation of energy we have approximately
And assijming the weight of the projectile, JV, to be con-
stant for the same piece
w: w'v.E'. E'wV^ \ V'^::X: X\
Therefore, in a S. B. mortar the charges are proportional
to the ranges. This is of importance in regulating charges
and works well in practice.
If in equation (9) we substitute the value of F in equa-
tion (5), we find, if we call g=32 approximately and ^=45°,
X=16 T' or
T= ^ (10)
which gives a rule for timing mortar fuzes.
RESISTANCE OF THE AIR.
To give an idea of the pressure exerted on projectiles in
the air and consequently of the insufficiency of the preced-
ing formulae for practical use, except in the cases cited; it
will suffice to say that a velocity of the wind of about 100
miles an hour is designated in the Ordnance Manual as a
"hurricane that tears up trees, carries buildings before
it, etc."
In projectiles moving with the high velocities now attained
the pressure is over 80 times as great as that assigned to
the hurricane.
EXPERIMENTS TO DETERMINE THE RESISTANCE OF THE AIR.
Experiments have been constantly made since Robins,
called the " Father of Gunnery," began to investigate this
subject about the middle of the last century. But these
:XX. EXTERIOR BALLISTICS.
gave untrustworthy results owing to the lack of suitable
velocimeters.
It is upon the investigations of the Reverend Francis
Bashforth, conducted under the auspices of the British
Government from 1865 to 1880, that our knowledge of the
effects of this resistance is based.
RESULTS OF EXPERIMENTS.
Resistance.
Bashforth's experiments demonstrate that the resistance
varies with the quantities shown on the following tabular
scheme.
'1. Area of cross-section or ^^, Chap. XVI.
2. Density of air.
3. k, Chap. XVI,|l. Meridian section]^ ^^^^^^^»
Resist-
ance
varies
with ^ page 2, viz.: |jj Velocity of projectile'.
1. That the resistance varies with the area is recognized by
all experimenters.
2. The effect of variations in the density of the air, whether
due to variations in barometric pressure, in temperature or in
humidity, or from the passage of the projectile through strata
of varying density, is allowed for m refined computations by
suitable coefficients. For this treatise the effects of such
variations are neglected.
3. Variations in k due to slight variations in the meridian
section are also neglected, although they may be similarly
corrected, see b below.
1. As to the Meridiafi Section^ viz, :
(a) Form of Head. — Bashforth in his experiments used
projectiles of the same calibre and weight, and having heads
of five different shapes. These were, 1st, hemispherical;
2d, hemispheroidal, with axes in the ratio of 1 to 2;
3d, ogival, radius of head 1 diameter; 4th, ogival, radius of
bead 2 diameters; 5th, fiat.
10 XX. — EXTERIOR BALLISTICS.
The resistance was greatest on the flat-headed projectile,
and least on the hemispheroidal and ogival of two diameters.
Rashforth concludes that the resistance offered by the air to
the motion of elongated projectiles is but little affected by
the more or less pointed apex, but depends chiefly upon
the form of the head, near its junction with the cylindrical
body of the shot. At this point the forms of the hemisphe-
roidal head, and of the ogival head of two diameters radius,
are about the same, and their resistances are nearly equal.
(/^) Form of Body. — Recent experiments by Krupp have
shown that the resistance varies also with the shapes of the
sides and rear of the projectile, and with the character of its
surface.
2. Retardation and Velocity,
Rashforth's method was one of interpolation founded on
the use of velocimeters of Class II, by which he determined
by means of finite differences the retardation of the pro-
jectile at certain points of its trajectory at which the velocity
was known.
Everything else being constant, the relation between the
retardation and the velocity was known for each of the veloc-
ities observed at any one fire. And by varying these veloc-
ities as by varying the initial velocity or the distance of the
gun from the targets, an indefinite number of velocities could
be observed and their corresponding retardations computed.
Finally, the law connecting the velocity and the retardation
could be deduced by analysis, or expressed by plotting a
curve of which the retardation and velocities are the coordi-
nate axes.
For the same velocity the retardation was found to vary
with (') the sectional density of the projectile, its f ) meridian
section and (') surface, and with the (*) density of the air as
XX. — EXTERIOR BALLISTICS. 11
affected by its temperature, barometric pressure and its
humidity.
Accordingly, such a law must for convenience be reduced
to standard conditions, that is, when (i) W (in pounds) = d^
(in inches), i. e., when we have the unit projectile^ and when
the (2) proportions and (3) surface of the projectile are well
defined, and the (^) density of the air is at a known standard.
Variations in these four conditions are subsequently
allowed for by suitable empirical coefficients of which we
shall deal with only that relating to the sectional density.
It may be stated however that Bashforth used a M. L. R.
gun firing studded projectiles^ the points having a radius of
IJ calibres. The more recent B. L. projectiles, having
sharper points and smoother surfaces, reduce the retardation
by 5 or .10 per cent. See page 10.
bashforth's method.
, He placed 10 targets at a constant interval of 150 feet=/.
This gave such a number of observations at each fire that
they served to correct each other by the principle of con-
tinuity, so that the final order of differences would be either
0, or would change very slowly. Examples of this are seen
in the methods used in correcting tables of squares, cubes
and of logarithms.
For this purpose the advantages of instruments of Class
II. over those of Class I. are obvious. Such instruments
ordinarily give only the velocity at some point between each
pair of targets. But Bashforth sought the velocity at the
target itself as follows :
Calling (7;,,) the velocity at the target which is at a distance
X from the gun
12 XX. — EXTERIOR BALLISTICS.
In measuring velocity it is customary to express j as a
function of t, in which t (one second) is the constant.
But when, as in these experiments, / is constant, it is
advisable to express the velocity by varying the value of/.
Consequently, calling r^ the retardation at the distance x
and observing that, since this is a negative acceleration, we
may neglect the minus sign resulting from differentiation,
we have "^
~di~~dF
^{ij=i^^^ (12)
The object of presenting the retardation in this form was
to make it an explicit function of the cube of the velocity
since Bashforth had reason to believe that the retardation
followed what is known as the cubic law.^
In order to apply equations (U) and (12) practically, it
is necessary to find by experiment such finite values for dt
and d'^t that, when substituted in the preceding equations
they will give proper values for v^ and r,. Or, calling these
finite values A/, ^nd AV,
^^=^ (11')
'■.= ~/r^l (13')
* The simplicity of such a law has always proved attractive to in-
vestigators of thir, subject. Sir Isaac Newton took it to vary with the
square of the velocity, and others with varying powers of the velocity
corresponding to certain limiting velocities.
Newton's law has recently been proved nearly true for the high veloci-
ties and smooth pointed projectiles now employed. It will be seen here-
after how Bashforth corrected the cubic law by an empirical coefficient
corresponding to the velocity.
XX. — EXTERIOR BALLISTICS. 13
DETERMINATION OF VELOCITY AND RESISTANCE.
Referring to Bashforth's experiments, let s denote the
distance from any origin to the first target. Then j + /
will be the distance from the same origin to the second
target and s-\-(n — 1) / the distance to the «'* target at the
distance x, and so on.
Also, let 4 denote the time from any origin until the
first target is reached. Then fs+(n-i)i will be the time from
the same origin until the n^'^ target is reached and so on.
Now, let ^1, 4> 4> etc., denote the 1st, 2d, 3d orders of
difference and d\ d'\ d"\ the successive terms in these
orders of difference so that 4'" will mean the third term
in the second order of difference and so on.
Then 4+i~4=^/> which will be the time of passage of
the projectile between the 1st and 2d targets and
4+21 4+1 = ^1 y
and d-l*—d^=d^ and so on.
We may therefore form the following table which may
be filled up from experiment as shown below numerically,
and graphically by the diagram, figure 5.
The dotted lines in the diagram serve to indicate the
successive orders of difference after the manner of the
brackets in the table.
TABLE.
No. of -p.. . Time of Orders of difference.
target. distance. ^^^^^^^ ^^ ^^ d^ . , , d^n-i)
1.
s
^8
2.
s + l
4-fi
3.
j + 2/
4+21
4.
5 + 3/
4+31
5.
j + 4/
4+41
[ dJ' etc.
\d.
14 :XX. — EXTERIOR BALLISTICS.
NUMERICAL EXAMPLE.
times.
^1
^.
^8
1.
S
3.0526
.1090
2.
j+150
3.1616
.1114
.0024
3.
J + 300
3.2730
.1138
.0024
1
4.
J + 450
3.3868
.1163
.0025
6.
^ + 600
3.5031
.1188
.0025
6. .y + 750 3.6219
From the algebra we have
^.+.=4+H' + « ^^/ + «^"~;y3~^^4' + etc.
Arranging the terms of the second member with refer-
ence to n which is arbitrary, we have
4+ni=4 + « W-i 4' + J 4'-etc.)
+ ^(4'-4' + etc.) (13)
Now /g^nb being a function of the space (s + nl)^ may be
developed by Taylor's formula. Hence we have
/s+ni=/(^ + «/) =^«+ ^«^+ -^T2- + ^'"-
or since, ds=lf
2
Equating the coefficients of the first power of n in the
second members of the two identical equations (13) and
(14), we have
<^/s=<^i'-J4'+^^3'~etc.=A4 (15)
:XX. — EXTERIOR BALLISTICS. 15
which is the finite value of dt^ for the constant increment
of 5.
In other words, and as shown by figure 5, if Bashforth
had taken d-l to be the increment of time at the first tar-
get corresponding to ds^ the velocity computed would have
been the mean velocity between the 1st and 2d targets and
would have been too small. Consequently this increment
is diminished by \ d^ . This makes the velocity too great,
so that \ d^ is added, the approximation increasing with.
the number of targets employed; since, under the same
circumstances, the greater the number of observations, the
more truly can the law be determined; or, mathematically
speaking, the greater will be the ± correction applied to
d^ since the greater will be the number of orders of
difference.
Therefore, for the target at the distance s or the first
target,
_ 2__ 150 ""^^
Similarly for the «'* target at the distance x = s-\- (n — 1)/
150 / ..„
""- - d^ - i 4° + ^4" - etc.- df, ^ (_,,, ^^^^
The number of the targets at which velocities could be
obtained is determined by the number of targets employed
and by the number of orders of difference which the law of
retardation permits. If n' be this number, then velocities
may be determined at (n — ;/) points.
Similarly, we have the coefficients of the second power
d% = d/—dj + etc. = A V„ (18)
and for the «** target
rx =
-^ AV, = p^.( d^^d,^ + etc. ) (19)
16 .XX. — EXTERIOR BALLISTICS.
Example.
The velocity at the 4th target in the preceding table is
1304: and the retardation 246.5.*
RESULTS OF THE EXPERIMENTS.
If the cubic law had held true for all velocities, the co-
efficient k in Equation (1), Chapter XVI, could have been
replaced by some explicit function of i^.
But while this was found to be nearly true for velocities
between 1100 and ]350 feet, it failed for velocities above
and below these limits, as Bashforth found by increasing
his velocities progressively from 100 to 2900 feet.
He accordingly introduced an empirical constant k* by
which to correct the departure from the cubic law so that
r — — /&' 7/
W '
and as k' is a very small quantity, he replaced it by
/ir= (1000)3 >^',
so that
Table I gives the value of K for the velocities named
therein and figure 6 is plotted from the indications of
Table I.
Example.
A 12.5 inch shell weighing 802.25 lbs. has a velocity of
1400. The total air pressure is 1394 lbs. and the retardation
is 55.96 at the instant that the velocity is 1400.
Figure 7 gives the pressure on what is called a circular
inch (that is a circle of which ^=1 inch) on spherical pro-
jectiles, curve A; on studded oblong projectiles of which
*Throughout this chapter velocities will be expressed numerically, as
the unit of velocity, or foot-second, may be understood.
XX. — EXTERIOR BALLISTICS. 17
the radius of curvature of the head is | d^ curve B ; and
on modern smooth b. 1. projectiles in which the radius = 2 d,
curve C, derived from recent experiments by Krupp.
In curve B two remarkable inflections are observed. One
at about 1090, the velocity of sound, and the other at about
2413, that of air rushing into a vacuum.
The first velocity marks the passage of the projectile into
a medium undisturbed by the explosion of the gun or by its
own passage. The second denotes the formation of a
vacuum in rear of the projectile which increases the pressure
to ajDout double that of the barometric pressure of the
atmosphere.
In firing at troops, particularly in sieges, it is important
to have the terminal velocity exceed that of sound, so that
the projectile may precede the warning sound made by its
passage through the air.
The irregularity of curves B and C shows the impossibility
of expressing by any simple law the relation between
velocity and pressure.
i
Final Velocity.
Figure 7 enables us to appioximate closely to the final
velocity of the projectile.
This term, which must be carefully distinguished from
the ter7ninal velocity (Chap. I), is that velocity which the
projectile has acquired in falling when the resistance of the
air becomes equal to the accelerating force of gravity. This
velocity is necessarily uniform and a maximum.
For example, a 64 lb. projectile, 6.3 inch in diameter, has
a weight per circular inch of 1.613 lbs. If it belongs to the
class of projectiles used by Bashforth, an equal and contrary
air pressure will result when a velocity of nearly 900 f. s.
has been acquired. But for more modern projectiles a
higher final velocity will result.
18 XX. — EXTERIOR BALLISTICS.
This velocity which formerly had only a theoretical signifi-
cance, is becoming important in consequence of the great
heights and high angles of fire now used in mortar firing.
The S. C. Mortar has thrown its shell over 3 miles into
the air with an angle of fall of about 75°.
The result can be reached more exactly by a method of
approximation based upon the fact that K enters into equa-
tion (20) in the first power while v is cubed. Consequently,
the first trial values of K will not greatly affect the result,
and we may finally find a velocity and corresponding value
of K which will satisfy the eqi^-^Hon
TRAJECTORY IN AIR.
GENERAL SOLUTION.
Notation.
Let O VR = S, figure 8, represent a trajectory.
Let V be the muzzle velocity in the line of departure.
ds
Let v= —j-he the velocity in the direction of the tangent
at any point of which the coordinates are x and y.
Let u be the horizontal component of the velocity v.
Let 7j\ v'\ u\ 2^", be the corresponding tangential and
horizontal velocities at the beginning and end of any arc,
the coordinates of the extremities of which are {x*^ y),
{x",y").
Let (p be the variable inclination to the horizontal of the
tangent to the trajectory; then u^v cos (p.
Let 6 and g9, measured as in the figure, be the particular
values of q) for the angles of departure and of fall.
XX. EXTERIOR BALLISTICS. 19
Let a and /? be the values of q} at the beginning and
end of any arc when the velocity is v' and v".
Then the figure shows that 6 — a — ^ or the angle in-
cluded between the tangents is the change in inclination
due to a change in velocity from v* to v'\
Similarly A=^— (—<») = ^+co is the total change in
inclination.
Let q) (read (p " dash ") be the inclination to the hori-
zontal of any chord of the trajectory.
Let 2/= = = u sec cp be the component velocity of
cos (p
V in the direction of the chord, and, as above, let v\ v" be
the component velocities in the direction of the chord at
the beginning and end of the arc (^',^')j (^"> ^")-
Let /,' /" be the times measured from any origin to the
instants when the velocities are respectively
( z/', z/"), P", v^), etc.
Note that /">/', v''<v'.
Let t—t"—t' for any arc and r=time to vertex, T\-\-
time from the vertex to R^ T^ be the whole time of flight, or
Similarly,
Let Jf', y, be the computed coordinates of the vertex
measured from 0\ and X^, K^, the computed coordinates
of the same point measured from ^, so that the computed
range, X=0 R=X' -^-X^.
The figure shows that the notation of z;', «', cp^ changes
from the ascending to the descending branch to z'^, u^^ cp.
This distinction will be observed throughout when the
branches are separately considered; but, when the trajec-
tory is considered as a whole, v\ z;", «&c., refer to the
beginning and ending of any arc.
20 XX. — EXTERIOR BALLISTICS.
Let the ordinate at D represent the height of a target at
the distance OD. Then DR is the dangerous space for
that target. If we aim at the center of the target this
evidently measures nearly twice the ± error permissible
in estimating the distance, as a measure preliminary to
determining the value of d required to strike the target at
some point of its height. See Chap. I., p. 3.
The dangerous space is known herein as D. S,
Eesolution of Motion.
Let AIR, figure 9, be some arc of the trajectory to
which //is the tangent at /, p is the radius of curvature,
g the acceleration due to gravity, r the retardation due to
the resistance of the air.
Then from the figure, for the horizontal retardation,
-— - = r cos (p (21)
and, from Mechanics, for the normal component of the
deviating force of gravity ,^^
(32)
-=gcos cp
, 1 dcp . dt
but - = -/- X -77
p ds dt
= — ^ and. therefore,
dt.v
dcp
(23)
Dividing Equation (23) by (21) member by member, we
have, after transposing,
dq>= 1^ (24)
XX. — 'EXTERIOR BALLISTICS.
21
Integrating between the limits (p=^a and ^=/5 and the
corresponding values of u^ we have
/3 y nf'
or
A ^g
du
rv'
From equation (21) we have by similar means,
du
r cos q)
or
du
cos q)
Similarly, from the relations between x,y, t, and Uy
u dt^=-
u du
r cos q)
or
u du
rcos (p
u du
or
r cos cp
u du
r cos cp
tan ^,
tan ^.
(25)
(25')
(36)
(26')
(27)
(27')
(28)
(28')
22 XX. — EXTERIOR BALLISTICS.
If these general equations (25-28) could be integrated,
they would give the change in the coordinates of an arc of
the trajector}'- (x^'—x^), (7"— j^') corresponding to a change
of horizontal velocity {u^—u")^ the time t required to
make this change, and the change of inclination d, corre-
sponding to the same change in the velocity.
But the second members contain three variables, u, cp^
and r, not connected by any law, and hence the integration
is impossible.
Bashforth's experiments, however, give the law connect-
ing u and r, and in order to avoid the difficulty arising
from the presence of the variable cp we assume for it a
constant mean value qy. That is, that on the same princi-
ple as that by which we have neglected the small vertical
component of the resistance, we now neglect the small
component velocity in a direction at right angles to the
chord, and suppose the length of the arc to be that of the
chord, although its curvature is retained.
COROLLARIES.
I. Equation (23) may be written
d(p __g cos (p
~dt V '
whence, by dividing member by member by
cos ^, w
dqp __g
dx
-—=zv COS cpf we obtain
sul
dcp _W
Calling esc- -^ — and substituting we have
dx 'Ze
(30)
XX. — EXTERIOR BALLISTICS. 23
Equations (29) and (30) express the rate of change of the
direction of the tangent to the trajectory, or the rate at
which the trajectory is becoming curved, as a function of
the range. Equation (29) ilhistrates the remarks, Chap. I,
top page 3, and Equation (30) explains the importance of
Chap. XVI, p. 1. These equations set forth a most import-
ant property of the trajectory in air.
Figure 10, >vhich is carefully drawn to a scale, represents
in curve A the trajectory in vacuo of a projectile fired with
e = 30° and V = about 1700 f. s.
Curves B and C represent the trajectories m air of spher-
ical projectiles as follows :
B. 15 inch ; W= 450 lbs. d = 14.87 inch. \V= 1700
C. 24 pdr. ; W = 26.92 lbs. d = 5.9 inch. 5 (9 = 30°
Since from Chap. XVI, p. 2, the elements of a trajectory
;When 6 and V are given depend on the ballistic coefficient
■— r, It appears that the 24 pdr. projectile would describe
the trajectory B if its weight were increased to 70.86 lbs.,
the calibre remaining constant; or, by reducing the calibra
to 3.637 inches, the weight of the projectile remaining con-
stant. The objections to this are given Chap. XVI, p. 4.
II. If in equation (29) we substitute for 2^ its value
\p g cos (pf we find
dg) 1 J dx
-~ = or d o) cos (Z) = —
dx p cos (p ^ ^ p
Integrating this equation between the limits -(- 6 and — w,
figure 8, corresponding to O and X, and assuming some mean
value of p = p' by which to measure the flatness of the tra-
jectory, we have as a measure of its mean curvature,
1 _ sin + sin 6>
7" - X ^^^^
24 XX. — EXTERIOR BALLISTICS.
Although from equation (22) and from experience it is
evident that, owing to the variable value of g cos cp^ with
the sight set for a certain range it is impossible to hit any
desired point of a vertical circle described about the gun
with the range as a radius; yet, as shown by equation (31)
and figure 11, if the altitude of the target or the angle of
sight s, be small, the decrease of g>' tends to compensate
for the increase of 6', so that sin 6' + sin w' may not differ
greatly from sin 6 -\- sin w : OX' = OX cos s will also be very
nearly equal to X, Under these circumstances the two values
of p' will not differ greatly from each other.
Under this assumption we may consider the mean curva-
ture of the trajectory to be constant or the trajectory to be
practically rigid, so that for small altitudes the elements of
the trajectory measured along the chord may be safely
assumed to be independent of the inclination of the chord
to the horizon.
Equation (30) shows that this assumption will increase
in truth when the sectional density and the muzzle velocity
increase, which is the present tendency. The principle
involved is of especial importance in the rapid fire of
modern small arms and field pieces, since it permits the use
for inclined ranges of sights graduated for horizontal ranges,
when the ± angle of sight is less than about 10°.
In such cases the change, s' figure 11, in the angle of
departure, may for a first approximation be safely taken to
be equal to s, and this change is automatically made by the
act of pointing.
Actually however, when s is positive, p' decreases and
conversely; so that in firing up hill the projectiles tend to
fall short and in firing down hill they tend to pass over the
object.
XX. EXTERIOR BALLISTICS.
NIVEN'S METHOD.
Various expressions have been deduced for the value of ;
that of Mr. W. D. Niven, F.R.S., obtained from an expand-
ing series, is one of the most simple and, for illustration, a
particular value of 0, deduced for equation (25), is herein
applied to all cases indifferendy.
The appendix to this chapter contains the means of arriv-
ing at more exact values of cp.
Under this hypothesis we shall adopt, as a sufficient approxi-
mation for small angles of 8 less than about 3°,
= ^, (32)
and for larger angles the approximation
— tan a -\- tan 6 ^,«„x
tan = J- -. *(33)
From the notation we have
u = V cos ; du =^ dv cos ; v' = u' sec 0, etc.
Substituting these values in equation (25), and replacing
r by its new value -^ -^r[TK()()] ' ^^ ^^^^
S = cos (pg
* These values of (p give good practical results.
26 XX. — EXTERIOR BALLISTICS.
In this equation ^ is expressed in circular measure, that is,
in terms of the ratio tt = 180°. To reduce it to the corre-
sponding number of degrees, d, we have,
Ttd
d:7c::d:180 or ^ = -^^.
loO
Substituting this value of S in the above equation, and
representing as hereafter the ballistic coefficient ^ by C, we
have, after reduction,
^ , cos 180^ (1000)
Ca =
7t
In this ^ is a function of v, and therefore changes between
the limits of integration. Means have, however, been found
for determining its mean value for limiting velocities.
The value so determined is nearly its arithmetical mean.
Therefore we have, calling this mean value K\
^^^cos0i8^o_oo): r-s^
Similarly, we have
And representing by s the length of the chord, the co-ordi-
nates of the extremities of which are {x' x") (/ y")
csj^' ry} (36)
We have also
X
II
s cos andji/ = y" — / = s sin (p
XX. EXTERIOR BALLISTICS. 27
These equations are in a form to be integrated, and Tables
II, III, IV have been computed for a projectile in which
^ = 1, as follows :
Assume any velocity v^ sufficiently low as the origin of in-
tegrals, and assigning proper values for K', integrate equa-
tions (34, 35, 36) between v^ and successive values of v'.
We thus obtain what are called angular /unctions dy> , time
functions^ r^> , and space functions, (Ti/ , which may be ex-
plained by reference to the time functions in Table II.
Explanation of the Tables.
Considering the acceleration to be positive. Table II may
be considered to express by its functions the several times
r, r', r", etc., required to give to a unit projectile, starting as
from rest, the several corresponding velocities under the ac-
tion of a variable force equal to the variable resistance of the
air.
Table III may be similarly understood to express the space
in feet <t, a', a", etc., over which such a force would have to
act in order to increase the velocity from some initial velocity
as 0, to the several corresponding velocities given.
It is evident that each function in each table might be
numerically diminished by the first function in its own table
without affecting the value of the table or the velocities to
which it applies, since it is only the differences between func-
tions that are considered.
Conversely, considering the acceleration as negative, if any
time function as r', figure 12, measured from any origin /^ ,
corresponds to a change v' — v^ in the velocity measured
from any origin v^ , and r" similarly corresponds to a change
r" — v^ , then r" — r' can correspond only to the particular
change &' — v". So that knowing r" — r' ^=^t, and either
z/ or v", we may determine the other velocity; and con-
28 XX.' — EXTERIOR BALLISTICS.
versely as to /, r', or r", without regard to whether the
difference is positive or negative.
Similarly for the angular functions. If any angular func-
tion d', figure 13, corresponds to a change v' — v^, and d"
to a change jy" — v^ , then 6* — d" = ^ will correspond to a
change v' — v".
In all cases we have two pairs of unknown quantities, of
which the difference between one pair and one of the other
quantities is needed to determine the remaining quantity.
These data are given by the conditions of the problem, or
are suppHed by certain assumptions to be hereafter explained.
Example from Table II.
The change of time (or time required) for a change of
velocity of 300 when the greater velocity is 1400 is 231.9883
— 230.5314 = 1.4569 sec. When the lesser velocity is 1400
it is 0.8697.
If in the first case the time from some given origin, say the
firing of the piece, until the velocity was reduced to 1400 was,
say, 2 seconds, then the time measured from the same origin
until the velocity fell to 1100, would be 3.4569 sec, and so on.
PRACTICAL FORMULAE.
For the ascending branch Equations (34), (35), (36) may be
written.*
Cd — cos (p{di> — 6-^") ; (I)
a = r-> — T^n ; (II)
Cs = a^> — <T~v". (Ill)
Whence from III,
Cx = Cs cos = cos 0(cr^/ — (Tin); (HI')
Q/ = Cs sin = sin 0(cr;,/ — (T^"), (HI")
* Similar equations serve for the descending branch.
XX. EXTERIOR BALLISTICS. S9
The Greek letters in the second members of the above
equations are the corresponding tabular functions found
respectively in Tables IV, II, III.
These tables are arranged like logarithmic tables. Except
■where small changes of the functions are considered, for sec-
tion-room work the column of differences need not ordinarily
be employed, the nearest function or velocity being taken.
It is evident that the nearer the chord is to the arc, the less
will be the difference v — v, and the more accurate will be
the result. In practice, it is considered sufficiently accurate
to divide the trajectory into two arcs, at the vertex.
For simplicity, and by the principle of the rigidity of the
trajectory, unless otherwise stated, the chord is taken hori-
zontal.
It is important to note that although ranges are generally
given in yards, the chords of trajectories (Chapter I) are ex-
pressed in FEET. Neglect of this frequently leads to failure in
practical work.
Example.
To illustrate the use of the tables in calculating the elements
of a trajectory, we will take the 100-ton Armstrong gun and
consider figures 8' and 14.
Data.
V= 1833; d = ll°50'=ll°.83i; PF=2005 lbs.; ^*=17 in.;
hence
C= 0.14414, log-^ = T. 15879, co-log -^ = 10.84121.
This quantity must always be determined before any other
work is attempted.
*The d above must be distinguished from the angle d elsewhere
discussed,
30 XX. — EXTERIOR BALLISTICS.
Elements required.
1. The remaining energy at any point or : e,
2. Height of trajectory at any point ot y.
3. Total range or X.
4. Angle of fall at end of range or qd.
5. The dangerous space, D. S. , for any range.
6. Time of flight to any distance or /.
7. Tinxe of flight for the whole range or T.
8. Inclination of the trajectory at any distance or <p.
9. Having the initial velocity to find the value of B to at-
tain a desired range.
etc. etc. etc.
1st. To find the remaining energy, we find the remaining
velocity as follows :
From figure 8 the change of from the origin to the
vertex is ^ = « = d. At this point /? = ; therefore, from
equation (33),
- tan Of 4- tan tan 11° 50'
tan <2!> = — ' —
2 2
= tan 5° 58' 50" = tan 5° 58'. 83.
As we shall have to use the logarithmic functions of 0, we
now tabulate them as follows ;
logs. co-logs,
sin T. 01783 10.98317
cos 1.99763 10.00237 = log sec 0.
To find v' we project V on the horizontal or determine
«' = Fcos B\ thence v' = «' sec 0, or «' = 1794, v' = 1803.9.
XX. — EXTERIOR BALLISTICS. 31
Now to find v'' we transpose equation (I) to read
COS
in which
Oj,' = 1803.9 •
In Table IV we find
di803 = 84°.8199
p. p. for 0.9 = 21
84°. 8220
Consequently, all the quantities in the second member
being known, we may write
14414
6-r= 84°.8220 - ll°.83i ^--l-**-^*
log'-i 1.99763
= 84°.8220 - 1°.7149 = 83°.1071.
From Table IV, again, we have for the velocity correspond-
ing to d = 83°.1071, v" = 1318 for the remaining velocity
at the vertex, and hence
«" = 1318 cos = 1310.8.
The origin is now transferred to the vertex, and we treat
the descending branch similarly to the ascending branch.
The angle a for this arc is evidently 0, and u^ = u" just
found, but the value of /? = g? required to find is unknown.
It is therefore necessary to assume a value for it. Equation
(29) shows that it will be greater than ^, and experience
4^
proves that it is nearly — or a? = 15°. 77,
3S XX. — EXTERIOR BALLISTICS.
If we assume an incorrect value, as will generally be the
case, the error is corrected by a subsequent operation. So
let us assume an incorrect value, or co= 16°, as a first ap-
proximation. Thence
tan 16° oo n/ K
tan (p = — - — = tan 8 9'. 5
— 4
I
and
v^ = 1310.8 X sec 8° 9'.5 = 1324.1 and (J- == 83°.1406.
Using equation (I) again, we have
*,„ = sr.im - ^-5^-5 16°
= 83°.1406 - 2°.3298 = 80°.8108;
and v^^ = 1061, u^^ = 1050, and v^^ , the velocity along the
tangent, := u„ sec. w = 1093. The vertical component of v
will be = «yy tan w = 301.
The component energies are generally useful for doing work
against targets which are nearly vertical, as the walls of vessels
or forts ; or horizontal, as the decks of vessels or the roofs of
magazines or casemates. We therefore find that while the
projectile started with energy in the direction of the tangent
or ^y = 46,700 foot-tons, it now has ^e/,, = 16,604 foot-
tons ; only about one third as much as when it started.
Its component horizontal and vertical energies are 15,320
foot-tons and 1260 foot-tons, respectively.
The steps of the problem can be clearly followed in the first
stages of Example I, which is given in the form used for
written recitation.
XX. — EXTERIOR BALLISTICS.
S3
la.
Data: F=1833; ^ = 11° 50' ; W=2005; ^=17 in.
Required U^,^^.
Statement of Steps.
Terms.
Quantities.
Functions.
Logs.
I- C = ^=0.14414
c
T
17^
2005
O.14414
2 . 46090
3 -30211
1.15879
c
IO.8412I
- tan 9
2. tan0=
= tan 5° 58'. 83
tan B
tan 11° 50'
2
9.32122
.30103
tan
tan 5° 58'.83
9.02019
cos
I
cos
sec "
9-99763
cos
10.00237
sin
I
sin
cos 6
sin
9.01782
I ,,
sin
10.98317
3. u'= F'cos = 1794
cos II 50
1794
3-26316
9.99067
3-25383
4. v' = u' sec (p = 1803.9
sec
v
1803.9
10.00237
3-25620
^■'-^■-'-"-co%-'^^'
h'
5l803.9
84.8220
C
d
n^83i
1. 15879
1.07300
sec
10.00237
I3I8
I. 7146
0.23416
83.1074
34
XX. EXTERIOR BALLISTICS.
Statement of Steps.
Terms.
Quantities.
Functions. Logs.
6. u' =: «^ = v" COS
= I3IO.8
COS
1318
1310.8
1 3-II992
9.99763
3.I1755
7.tan^='^"/ = 8"9'.5
tan /?
tan
cos
sec
sin
I ~~
tan 16°
tan 8° 9'. 5
cos "
sec '*
sin '*
I .,
sin
9-45750
.30103
9.15647
9-99558
10.00442
9.15201
sin
10.84799
8. vi = u sec = 1324. 1
sec
1310.8
1324-2
3-11755
10.00442
3.12197
9. d- = (5- — CJ sec
= 1061
d
sec
^1324. a
16"
I06I
83.1411
2.3298
1. 15879
I. 20412
10.00442
The determination of g is
omitted.
0.36733
80.8113
XX. EXTERIOR BALLISTICS.
35
lb.
Data as in la.
Required » at 1000 yards = 3000 feet.
Statement of Steps.
Terms.
Quantities.
Functions.
Logs.
J. Determine whether to
use or by finding
whether 3000 is < or >
X' .:
cos
I
C
X'
O"i803-9
15045
44456.3
42275.8
9.99763
jr'=cos0(a--,-o--„)X^
= 15045 ft. =;= 5015 yds.
.*. use
2180.5
3.33856
IO.84121
4.17740
2. 0--,, = (T-, — Cx sec (p
v" = 1697
sec
3000
1697
44456.3
434-8
I. 15879
3.47712
10.00237
2.63828
44021.5
36
XX. — EXTERIOR BALLISTICS.
Data as in la.
Required V from data of ascending branch.
Statement of Steps.
Terms.
Quantities.
Functions.
Logs.
y:=Y'
= sin 0(o--,-o--„)i
sin
9.01782
^1576.1 feet.
^i'
Cri803.9
44456.3
^-."
cri3i8
42275-8
2180.5
3-33856
C
IO.84121
v
1576. I
3-19759
Similarly we may find from the value of that
r, = 1713 feet.
The difference, 1713 - 1576.1 = 136.9 is evidently due to
the error in our assumption of the value of gj, and therefore in
our deduced value of ; the effect is to increase the range as
shown by figure 14.
This leads to the means of correcting od to be explained.
3. To find the range.
With the assumed value of gd and we find X^ by the
method described in lb, or X^ = 11949 feet.
Ave also have X' = 15045.4 ''
Z = Z'-|-X, = 26994.4 ''
But this range is too great by the distance B^C, figure 14.
To find this distance we assume that this short arc coincides
with its tangent, which by assumption makes an angle of 16°
with the horizon,
XX. — EXTERIOR BALLISTICS. 37
Therefore
B'C = -i??^ = 477.4 ft. and X, = 11471.6 ft.
tan 16
and X = 26517. ft. = 8839 yds. = 5 miles + .
4. To find the incHnation at the end of the range or the
angle of fall, oo.
We can vouch for only the elements of the trajectory in the
ascending branch, but if we can determine the range as by
firing or by the method just described, we may approximate
closely to the angle of fall.
For
V tan GD
tan0 = ^ = — -;
. •. tan G? = V and Ce9 = 15° 20' 28".
^/
In the example this gives a difference of but 6. 8 feet in the
two values of K, which difference can be further reduced to
by successively approximating to the true value of oj, or
G) = 15° 18' 12" ; and therefore ±^=7° 47' |i and ~v, ==
1323, z7, = 1067.3, X, = 3840 yds.
These values will be hereafter employed, since it is most
important to have a correct knowledge of the elements of the
trajectory at its further end.
Practical Methods for Detennining w.
1. Fire through a screen near the point of fall, and note the
height /if of the hole above the horizontal plane on which
the projectile strikes, and the distance of its impact, d, beyond
/i
the screen. Then tan w = -— nearly.
38 XX. — EXTERIOR BALLISTICS.
Or note the inclination of the shot-holes in snow or in
horizontal targets composed of double layers of boards.
2. Determine the range OR, figure 15, for a given value
of Q, and then increase ^ by a slight increment AB. This
will increase OR by AR = RR\
Then assuming HR' to be straight and parallel to the tan-
gent at R,
. RR Rt^nAf)
'^'''^ = RR' = -AR~'''^'^y-
3. Determine the range under two sets of conditions differ-
ing only in the height, /i, of the gun above the horizontal
plane. Then if this difference be relatively small with regard
to the range from figure 16, tan go = --t-= .
4. Figure 17 shows how this would practically be done,
since it would be difficult to raise a gun sufficiently without
displacing it horizontally :
tan 6) =
0' R> — O R.
Application,
Range-tables are constructed to give all the principal ele-
ments of the piece, charge, and trajectory for different ranges.*
The following method and figure 18 show how, having a
range-table, we may determine the co-ordinates of the vertex.
Find in the range-table two angles of departure and of fall
a and j3, such that their sum =: 6. Then by the principle of
rigidity S will be the chord to the vertex, and S cos /? = X',
and 5 sin i3 - Y'.
* See Chapter XXX, pages 9, 52.
XX. EXTERIOR, BALLISTICS.
5. To find the dangerous space at any range, or the hori-
zontal distance over which a target of given height would be
struck.
We have in this case to find the distance at which the height
of the trajectory is equal to that of the target. The target will
evidently be struck when situated at this point, since the tra-
jectory passes through its summit, and it will also be struck
if situated at any point intermediate between this and the end
of the range. Hence if D, figure 8, be the target the dan-
gerous space is DR.
The simplest way of determining this is as follows. Sup-
pose the target to be 30 feet high, then from (HI")
cr;. = O-1067 3 + -T—r = 40626. 4 + 31.9 = 40658. 3 = (T^^^,^ ;
sm
or z;, = 1070.9.
Similarly
x = DS- 219. 2 ft. = 73 yds.
If the proper value of w has been found, the same result
may be obtained by working downward from the vertex, tak-
ing y = 1576.1 — 30 r= 1546.1, and
Ovn = (^v. ■ — 7 = CT ,070 3 as before.*
sm
The accordance of these methods tests the accuracy of the
determination of w ; but without exacting the somewhat labo-
rious process required for this determination, a check of the
accuracy with which the dangerous space has been determined
may be had by observing that the angle whose tangent is
equal to the height of the target divided by the dangerous
space is greater than and less than w.
* Or taking the trial values assumed for the descending branch , viz^
Vy = 1113 ; J/ ^ = \S24.2'yV yy=z 1061 we have as an approximation
^ = 1683 J v'^^ =5 1064 ',xs=a 202.6 ft.
40 XX. — EXTERIOR BALLISTICS.
The dangerous space is one of the most important proper-
ties of a trajectory, since, Chap. I, it measures the chances of
striking an object at a distance which in warfare is only ap-
proximately known.
The flatter the trajectory at its further end the greater is the
permissible margin of error in estimating the range before
aiming.
The principles of Chap. XVI and equation (30) illustrate
the importance of high velocities and high sectional densities,
since if one projectile, a, figure 19, having less sectional den-
sity than another, projectile b, be projected with equal ener-
gies at the same ranges, although the trajectory of a may be
flatter than that of b at the start, yet near the target the D.S.
of b will be greater than that of a, if the target lies beyond the
intersection of the two trajectories.
Although the method above described is generally followed,
and is best suited to cases where w is accurately known, a
simpler and probably a more accurate plan is hereafter given,
page 44.
6. To find the time of flight to any distance. Take the
distance as 1000 yards = 3000 feet, as in \b. We have from
equation (II) and data previously computed
/ = (r^. — r^//) ^ = (ri803.9 — ^1097) ^ = 1- '^^03 sec.
7. To find the time of flight for the whole range.
1st. We proceed as in No. 3, using equation II and the
corrected value of v^^ = 1067.3.
T = (t;/ — r;,//) - = 9.8432 sees,
and r, = (r;, - nj i = 9.8569
r=r + T, =19.7001.
XX. — EXTERIOR BALLISTICS. 41
2d. Or we may pass directly to the point of fall, as follows:
rr=(r;.-r7ji= 19.566,
which is sufficiently accurate for most purposes.
3d. If the true value of oo or v^^ is not determined, we may
still approximate to T^ by finding the time 4 required for the
projectile to pass over the correction of the range determined
477
in No. 3, with the velocity u^^ or 4 = — — - = 0.454 sec.
jLUoU
Therefore having with the assumed value of cl? = 16° found
T, = 10.266, its corrected value is 9.812, which added to 7"
makes T= 19.6552 sees.
4th. Or, if we neglect the difference in time of passage
over (y, — Y' )j due to the resistance of the air, since
/, = \/?(n/k_ v'f), we obtain 4= 0.4186 and T, =
^ g
9.8474 which is a closer approximation than 9.812, since
T, > T!
Scholium.
Equation (23), which may be written
cos g
or
gj^ COS0 gj^ COS0
shows that, although for the descending branch the mean
value of V is less than that for the ascending branch, the in-
crease in the value of shown by equation (29), and the con-
sequent decrease in cos (f>, may compensate and keep the ra-
42 XX. — EXTERIOR BALLISTICS.
tio nearly constant ; so that as far as iifue only is concerned
the trajectory may be supposed to be in vacuo.
That this is practically so appears from the equality of T
and T, in the above problem and in those solved by other
methods.
Consequently, and particularly for small values of A, when
the vertical component of the velocity is so small that it may
be safely neglected, the time to the vertex may be safely taken
as half the whole time of flight, and in cases of necessity
Equations (6) and (7) may be employed.
For example, for this case, which is certainly an extreme
one, if we substitute the value oi T — 19.70 sec. in the equa-
tion K = "-^we obtain for Y a value 1561, which is only
15.2 feet less than that before deduced. When the value of
A is large, the equations of the trajectory in vacuo cannot be
indiscriminately applied.
Principle of the Vertex.
From the above follows this important conclusion : If we
represent the time to the vertex by /^ (read / vertex), the ve-
locity at the vertex by z^y^, and the corresponding time function
T
by r^, then /a = y.
Then we have from equation (II), generalized as to notation,
Ct. — ^ — '^^LZLEul ~ r ' — r .
and
XX. — EXTERIOR BALLISTICS. ^ 43
Or, the time function of the velocity at the vertex is equal to the
arithmetical mean of the time functions of the velocities at each
end of the arc.
This, which may be termed the principle of the vertex, is of
great value in approximate solutions.
If we know the time interval / corresponding to two veloci-
ties, of which one is known, then the time function of the ver-
tex of any arc may be determined as follows, from the above
and Equation (II) :
Cl , Ct ,^^-
r A = r^' - Y = -^v" + y . (37)
8. To find the inclination at the top of the target, which
we will now assume to be a rampart 30 ft. high, so that what
was before the dangerous space will be the safe space.
From equation (I), with the corrected values given, page 37,
we have
d=cos(l)iS--6-\l,= -0°, 35674= - 0° 21' 24".*=
= cos IS 6- \ 77 =
therefore0 = a7-^ = 15°18'12'"-O°21'24" = 14°56'48".
Or, working down from the vertex, = 14° 57'. The
true safe space will, owing to the increasing curvature, be
30
somewhat less than ; ., ,o ^r^, = ^^^ ^t-
tan 14 57
The difference between this result and that before reached
for the dangerous space shows the limitations of the ordinary
method, and is probably due to not having found the correct
value of for the function d, as explained page 25 and in
the Appendix.
41 1
* = cos T 47' ^2 (^1070. 9 — ^1067. 3) ^.
44 XX. EXTERIOR BALLISTICS.
A closer approximation to the dangerous space would
probably be found from the principle of the vertex, as fol-
lows:
Assuming the rigidity of the trajectory, the tangent at the
vertex of any elementary arc is parallel to the chord. So that,
finding the inclination 0/^, at the vertex of the arc in rear of the
target the dangerous space may be found, since
D.S. = height of target X cot 0/,.
By using the corrected values pages 37 and 39,
r -\- T
w 1070. 8 I 1067. 3
we find
V^ = 1069.1, (^,„,,., --(^,„,,.3 = 0°.0260,
whence
t/= 0°.1787 and (p^ =15. 30 J - 0.1787 = 15° 7', 47.
D.S. = 111 feet.
This method enables us to obtain the dangerous space quite
closely for an approximate value of v^^ , and to determine an
important element without requiring the tedious correction
mentioned, page 37.
Assuming then v^^ = 1061, the velocity along the tangent is,
since u^^ = v^^ cos (f) = v„ cos w.
V,^ cos
^"^■^^^^ = 1^93,
the vertical component of which is v,, sin w = 1093 sin 16" =
301.
The time of passage over the height of 30 ft. with this ve-
locity will be / = 0.09961 sec, though it will actually be a trifle
less, and -- = 0.0071.
4
XX. — EXTERIOR BALLISTICS. 45
Ct
Now since r^ = 7^./ + - = r,„,, + 0. 0071 = 230. 2330,
.-. v,^ =: 1061.8.
Also, since d = cos (c^ioei.e - ^loei)^ = 0.0845,
30
d>. = 16° - 0.0845 =15° 54'. 9 and^ = 105 feet.
^'^ tan
This is much nearer the true value than the result given by
the method described page 39.
Very nearly the result arrived at by the method above de-
scribed, viz., 105 feet, would be obtained by taking for the time
of passage / = \J g \ v'1576.2 - |/1546.2l = 0.0947 sec.
9. Having the initial velocity and the value of C, to find
the angle of departure necessary to attain a given range, and
other elements.
The conditions of this problem, which is a frequent one in
practice, require (page 6) that the rigidity of the trajectory be
assumed and that the principle of the vertex be applied.
Solution.
1. The piece is supposed to be fired with its axis horizontal,
and we compute the elements of the trajectory as if it were
the descending branch of an imaginary trajectory.
Then we revolve the trajectory upward until the chord
becomes horizontal. By the principle of rigidity S is
taken = X, which, to test the accuracy of the method, we
take = 26517.24 feet, as previously determined.
-f^'" m THE -)^^:*v
c
iiiTh&
46 XX. — EXTERIOR BALLISTICS.
From equation (III) we have
(Tj,^^ = (Tv' — Cx, or v^^ = 1081.
^rom equation (II)
^A = i (^,833 + ^:o8i) or v^ = 1348.
Then from equation (I), since 6 = and cos 0=1,
d = 1-:^A = 11° 26' 13" = e.
Compare these results with those previously deduced.
2. In such a case, to determine the angle of fall and the
dangerous space, we would proceed as follows :
Find D, in degrees, the total change = 6 -\- go, hy saying
■^ = (^:,3. - ^.08:) ^= 26°.29 = 26° 17' 24";
then a? = Z> - ^ = 14° 51'. 2 and
SO
It is evident from the above, that, knowing the angle of fall
required to strike near its foot a scarp protected by a cover
at a known height and separated from it by a ditch of known
width, it is only necessary to know the distance of the breach-
ing battery from the wall, and the ballistic coefficient of the
projectile, to determine approximately the value of 6 and of
the initial velocity or charge of powder required to strike the
wall at nearly the desired spot, with a required remaining
energy.
It was by some such method that the German artillery
breached at hitherto unknown ranges the invisible walls of
Strasburg. See problem page 51.
XX. — EXTERIOR BALLISTICS. 4?
Thus, by the principle of rigidity,
From CX = ay — c^ determine V and weight of charge.
** CD^Sy- d^ *' D.
*' conditions ** go.
** D — GO "6.
MODIFIED FORMULA.
For low angles of departure and high velocities and sec-
tional densities giving small values of A, the principle of
rigidity permits the formulae on page 28 to be written
Cd •= Sy — 6^ , (A)
a = Ty — T^; (B)
0= ay — (7^,. (C)
In these formulae, since sin = 0, we must resort to Equa-
tions (0) and (7) as explained page 7, or
y=^(T-(): (6)
y=^^ (7)
The propriety of this assumption appears from applying it
to the case of the 100-ton gun, assuming the velocities to be
horizontal and solving without reference to the vertex. Thus,
assuming as before (o = 16°, we have from (A), using whole
numbers, 27°.83 = (6,^ — 6„) ~ .-. 2/,, =1061.
Similarly we find T= 19.94 sec. and X = 8983 yards, lead-
ing, as seen by comparison, to but slight errors providing that
0) has been correctly assumed.
So that we may have confidence in the results obtained by
the use of Equations (A), (B), (C), when v does not differ
much from u , and, when v sin (p is so small that it may be
neglected, we may use Equations (6) and (7).
48 XX. — EXTERIOR BALLISTICS.
Example.
The Springfield rifle and ammunition give the following
data :
W= 500 gr. = 0.071428 lbs. ;
Diameter of projectile = 0.455 inches in flight •
V= 1300 ft.
By experiment we find that for a range of 500 yards as
measured by the breech sight = 1° 17' 18".
1. Find GO.
1st. From (C) determine v^ = 869
2d. ** (A) " D = 2° 40' 23".
3d. '* D-d'' fi9 = l°23'05".
2. Find r.
1st. From {B) determine T= 1.467 sec.
2d. " (7) '' i"=8'.662 feet.
3. Findj^/ at 400 yards = 1200 ft.
1st. From (C) determine v at 1200 ft. -= 921.
2d. " (B) " / to 1200 ft. = 1.132 sec.
3d. " (6) and T above determine 7 = 6.105 ft.
By this means we may construct a drawing of the tra-
jectory.
4 Find the 'Dangerous Space at 500 yards.
The target is a man 5 ft. 8 in. (5§ ft.) high = y. The gun
is supposed to be fired lying down (from the ground) and to
be aimed at the feet of the man.
1st. Reckoning from the summit of the trajectory we have
^1 ^ y "~ = 0.4313 for the time from the vertex to
T
the top of the man's head, and -^ — /, = time over D. S. =
0.3022 = f,
2d From /' and (B) determine v at target = 915.
3d. From (C) determine D. S. = 267 ft. = 89 yds.
XX. — EXTERIOR Ballistics. 49
It is generally 1 etter to work backward from the point of
fall than forward from the gun, as the results are more con-
sistent if the data are supplied from only one branch of the
trajectory. See page 39.
However, this does not apply in the above case, in which
the vertical resistance of the air is wholly neglected, so that
the same results would follow from either course of procedure.
See page 41.
Alternate Solution,
If in Equation (6) we supply the value of T previously
deduced, and solve the resulting quadratic equation, we shall
have two values of /, one of which gives the time for the
projectile to rise to the height of j/, and the other which gives
the time for the projectile to rise to the vertex and to fall
to this height above the horizontal plane, so that there will
be two dangerous spaces, the interval between them being
the safe space.
It is evident that as the range decreases, the other conditions
remaining constant, the safe space finally becomes 0. The
resulting dangerous space will then be continuous and a
maximum.
The maximum dangerous space for a given small-arm thus
depends upon a physical constant, — the height of a man ;
and assuming, as above, the mean height of a man to be 5f
feet, the maximum dangerous space will be a function of p',
page 23, and will be a convenient measure of the joint power
of the gun and ammunition. The height i^will = 5f feet.
5. Find the maximum Dangerous Space for the preceding
ballistic condidons.
Sec.
1st. From (7) determine T= 1.187.
2d. '' (B) *' z;=912
3d. '' (C) ** X= 416.6 + yds. = max. D. S.
50 XX. — EXTERIOR BALLISTICS.
APPENDIX A.
The value of was obtained approximately by Mr. Niven
from an expanding series. (See Proceedings of the Royal
Society of England, 1887; No. 181.)
The value of to be used with Table IV for changes of
inclination is that given in the text for high angles of depart-
ure, say ^ > 5°.
For 6* < 5° may be taken =. ^ ~l -.
For the other tables he takes
though, where greater approximation is required, for changes
of time he uses
APPENDIX B.
Problems.
The answers given below result from the use of the modi-
fied formulae.
1. The 3.2-inch steel b. 1. rifle. Weight jof shell or shrap-
nel = 13 lbs. I. V. = 1634.
Determine : (1) The distance at which v of shrapnel will be
500.
(2) Time of flight for this distance.
(3) Angle of departure for this range, supposing
the shrapnel to explode 40 ft. above the
object, or the angle of sight — y'.
Answers : (1) 19,106 ft. or 3.62 miles.
(2) 24.6 sec.
(3) 24'^ 44'.
XX. — EXTERIOR BALLISTICS. Bl
2. A target is to be placed on Cro' Nest. The distance
from the sea-coast battery to target is 1990 yards ; height of
target above battery is 237 feet. . Determine the angle of
departure necessary to strike the target, using the 8- inch con-
verted rifle. ,/ = 7. 95 inches ;
Weight of projectile = 180 lbs. ;
I. V =1414. Answer: 5° 45'.
3. The 6-inch b. 1. rifle requires according to the range
table an elevation of 1° 51' and a muzzle velocity of 1850 f. s.
to strike an object at a distance of 2U00 yards. On firing the
range obtained was only 1800 yards, and investigation showed
that the powder was damp.* What additional elevation would
be necessary for a range of 2000 yards ? tV= loo lbs.
Answer : 0° 28'.
4. At the siege of Strasbourg in 1870, the Germans wished
to breach the scarp wall of an outwork at 2000 yards distance ;
the ditch was known to be 50 feet wide, and the shell were
to strike 12|- feet below top of counterscarp wall. An 8-inch
howitzer firing a projectile weighing 180 lbs. with a muzzle
velocity of 700 f. s. was employed.
Required the striking velocity and the angle of departure
A i 616 f. s.
Answer : i
(11° 47'.
5. At a range of 1200 yards a 64-lb. shell grazes the top of
a traverse 8 feet high. How far beyond the traverse will the
shot strike the ground ?
^=6.171 inches;
Weight of projectile = 64 lbs. ;
I. V. = 1260 f. s.
Answer : 153 feet or 51 yards.
6. A Martini-Henry rifle-bullet strikes a vertical target at
500 yards at a certain spot when the muzzle velocity is 1353
f. s. How much lower on the target will the same projectile
*See proportion, foot p. 7.
^2 XX. — EXTERIOR BALLISTICS.
Strike if the muzzle velocity is only 1300 f. s., the elevation
and other conditions remaining the same ?
^ = 0.45 inch.
Weight of projectile == 480 grains = 0.06857 lb.
Answer : 21|^ inches.
7. Using the Hebler rifle, determine the maximum con-
tinuous dangerous space for a man kneeling.
d =0.296 inch;
w - 225 grains = 0.03214 lb.;
I. V. =1942f. s.;
Height of a man kneeling = 42 inches.
Compare with Springfield rifle :
d =0.45 inch ;
w — 500 grains = 0.07142 lb.;
I. V. = 1316 f. s.
Answer: Hebler rifle, 458.0 yards.
Springfiold rifle, 340.7 ''
8. A 3-inch Eureka shell, weight 9 lbs., fired with 2 lbs. of
powder, has an I. V. = 1495 f. s. With what charge should
a 10-lb. shell be fired to have at 407 yards the same remain-
ing velocity that the full charge gives at 2500 yards }
Answer: 11.5 ounces.
9. A 3.2-inch shell weighing 13 lbs. is fired with a muzzle
velocity = 958 f. s. The target is at a distance of 407 yards,
and the angle of sight is 4° 1'. Determine the necessary
breech-sight elevation and the quadrant elevation.
Answer: e = V 19'.
q = b° 20'.
10. A 3.2-inch shell weighing 13 lbs. is fired with I. V. i=
986 f- s. How high above the gun should be placed a hori-
zontal bar at a distance of 80 feet, so that the shell shall
strike the bar and hit a target on the same level as the gun,
and at a distance of 1200 yards. Determine also the neces-
sary breech-sight elevation.
Answer: Height = 4 ft. 6.5 ins.
^ = 4° 0' 22'^
XX.— EXTERIOR feALLlSTlCS.
BALLISTIC TABLES.
Table I.
Value of K for the Cubic Law of Resistance, Ogival-headed
Projectiles {1%, diameter heads).
Velocity.
Value
ofK.
Velocity.
Value
OfK.
Velocity.
Value
OfK.
Velocity.
Value
OfK,
f.8.
f.s.
f.s.
f.s.
400 ....
148
880 ....
75
1360 . . . .
106
7
1840 ....
75
2
410 . . . .
145
2
890 ....
75
1370 . . . .
106
3
1850 ....
74
7
420 . . . .
142
5
900 ....
75
1380 ....
105
8
1860 ....
74
2
430 . . . .
139
8
910 ..:.
75
1390 . . . .
105
3
1870 ....
73
6
440 ....
137
2
920 ....
75
1400 . . . .
104
7
1880 ....
73
1
4r)0 . . . .
134
6
930 ....
75
1410 . . . .
104
1
1890 ....
72
6
460 ....
132
940 ....
75
1420 . . . .
103
5
1900 ....
72
1
470 . . . .
129
4
950 ....
75
1430 . . . .
102
9
1910 ....
71
6
480 ....
126
9
960 ....
75
1440 . . . .
102
3
1920 ....
71
2
490 .. .
124
4
970 ....
75
1450 . . . .
101
6
1930 ....
70
a
500 . . . .
121
9
980 ....
75
1460 . . . .
100
9
1940 ....
70
4
510 . . . .
119
6
990 ....
75
1470 . . . .
100
1
1950 ....
70
520 . . . .
117
3
1000 ....
75
1480 ....
99
4
1960 ....
69
7
530 ....
115
1010 ....
75
1
1490 . . . .
98
6
1970 ....
69
4
540 . . . .
112
8
1020 ....
75
3
1500 . . . .
97
9
1980 ....
69
2
550 . . . .
110
7
1030 ....
76
7
1510 . . . .
97
1
1990 ....
69
5G0 . . . .
108
7
1040 ....
80
8
1.520 . . . .
96
2
2000 ....
68
8
570 . . . .
106
7
1050 ....
87
3
1530 . . . -
95
3
2010 ....
68
6
580 . . . .
104
6
1060 ....
94
1540 . . . .
94
4
2020 ....
68
4
530 . . . .
102
5
1070 ....
98
7
1550 . . . .
93
6
2030 ....
68
3
600 . . . .
100
5
1080 ....
102
2
1560 . . . .
92
8
2040 ....
68
2
610 . . . .
98
6
1090 ....
104
9
1570
92
2050 ....
68
1
620 ....
96
8
1100 ....
lOG
9
1580 ....
91
2
2060 ....
68
630 . . . .
95
1
1110 ....
108
4
1590 ....
90
4
2070 ....
67
9
640 . . . .
93
5
1120 ....
109
2
1600 ....
89
7
2080 ....
67
9
650 . . . .
91
9
1130 ....
109
6
1610 ....
89
2090 ....
67
8
660 . . . .
90
5
1140 ....
109
6
1620 ....
88
3
2100 . . .
67
8
670 . . . .
89
1
1150 ....
109
6
1630 . . . .
87
6
2110 ....
67
7
630 . . . .
87
7
1160 .. .
109
6
1610 . . . .
86
9
2120 ....
67
6
69S ....
86
3
1170 ....
109
6
1650 . . . .
86
2
2130 ....
67
6
700 ....
84
9
1180 ....
103
6
1660 . . . .
85
5
2140 ....
67
5
710 . . . .
83
7
1190 ....
109
6
1670 . . . .
84
8
2150 ....
67
4
720 ....
82
6
1200 ....
109
6
1680 . . . .
84
2
2160 ....
67
3
730 . . . .
81
6
1210 ....
109
6
1690 . . . .
83
6
2170 ....
67
2
740 ....
80
6
1220 ....
109
6
1700 . . . .
83
2180 ....
67
2
750 ....
79
6
1230 ....
109
5
1710 . . . .
82
4
2190 ....
67
1
760 ....
78
7
1240 . . .
103
5
1720 ....
81
8
2200 ....
67
770 . . . .
78
1250 ....
109
4
1730 . . . .
81
2
2210 ....
66
9
780 ....
77
4
12f30 ....
103
3
1740 . . . .
80
6
2220 ...
66
8
790 ...
76
8
1270 ....
103
2
1750 ....
80
2230 ....
66
8
800 ....
76
2
1280 ....
103
1760 . . . .
79
5
2240 ....
66
7
810 . . . .
75
6
1290 ....
108
8
1770 ....
78
9
22-0 ....
66
6
820 ....
75
2
1300 ....
108
6
1780 ....
78
4
2260 ....
66
5
830 ....
75
1
1310 ....
lOS
4
1700 . . . .
77
8
' 2270 ..
66
4
840 . . . .
75
1320 ....
10^.
1
noo ....
77
3
, 2280 ....
66
2
850 . . . .
75
1330 ....
107
8
1810 . . . .
76
8
2290 ...
65
9
860 . . . .
75
1340 ....
107
5
1820 . . . .
76
2
2300 ....
65-5
870 . . . .
75
1350 ....
1
107 1
[ 1830 ....
75-7
u
5C5t. — EXTERIOR BALLISTICS.
Table II.
Time and Velocity Table, Ct = r^, — r^„.
V.
1
2
3
4
5
6
7
8
9
Difl:
f.8.
40
41
42
20 5-0299
6-0554
7 0276
sees.
5-1349
6-1550
7-1?,'^0
sees.
6-2393
6-2540
7-2159
sees.
5-3432
6-3525
7-3093
sees.
5-4466
6-4505
7-4022
sees.
5-5494
6-5480
7-4947
sees.
6-6517
6 6450
7-5867
sees.
5-7534
6-7414
7-0782
sees.
5 8546
6 8373
7-7693
sees.
6-9553
6-93^7
7-8599
+
-1028
-0975
-0925
43
44
45
20 7-9501
8-8272
9-6622
8-0398
8 9125
9-7435
8-1291
8-9974
9-8244
8-2179
9-0819
9-9050
8-3063
9-1660
9-9852
8-3942
9-2497
*0-0651
8-4817
9-3330
*0 1446
8-5687
9 4159
*0-2237
8-6553
9-4984
*0-3025
8-7415
9-5805
*0-3809
-0879
-0837
•0799
46
47
48
21 0-4590
1-2205
1-9487
0-5367
1.2948
2-0198
0-6140
1 3687
2-0906
0-6910
1-4423
2 1611
0-7677
1-5156
2-2313
0-8440
1-5886
2-3012
0-9200
1 6613
2-3708
0-9956
1-7336
2-4401
1-0709
1-8056
2-5091
11459
1-8773
2-5779
-0763
•0730
-0699
40
60
61
21 2-6464
3-3159
3-9592
2-7146
3-3814
4-0221
2-7825
3-4466
4-0848
2-8501
3-5116
4 1472
2-9174
3 5763
4-2094
2-9845
3-6408
4 2713
3 0513
3-7050
4-3330
3-1178
3-7689
4-3944
3-1841
3 8320
4-4556
3-2501
3-8960
4-5165
-0671
-0645
-0619
62
63
64
21 4-5772
5 1719
5-7450
4-6377
5-2302
5-8012
4-6979
5-2882
5-8572
4-7579
5-3460
5-9130
4-8177
5-4036
5-9686
4-8773
5-4610
6-0240
4-9367
5-5182
6-0792
4-9958
5-5752
6-1342
5-0547
5-6320
6 1890
6-1134
5-6886
6-2436
-0596
-0574
-0554
55
66
67
21 6-2980
6-8311
7-3460
6-3522
6-8834
7-3965
6-4062
6 9355
7-4469
6-4600
6-9874
7-49-71
6-5136
7-0391
7-5471
6-5670
7 0907
7-5970
6-6202
7-1421
7 6467
6-6732
7-1933
7-6962
6-7260
7-2444
7 7456
6-7786
7-2953
7 7948
0534
-0516
•0499
68
69
60
21 7-8438
8-3271
8 7957
7-8928
8 3746
8-8417
7 9417
8-4220
8 8877
7-9904
8-4692
8-9334
8-0389
8-5163
8-9791
8-0873
8-5632
9 0246
8-1356
8 6100
9 0700
8-1837
8-6566
9 1152
8-2316
8 7031
9 1603
8-2793
8-7494
9 2052
-0483
0468
0454
61
62
63
21 9 2501
9-6908
22 0-1183
9-2947
9 7341
1604
9 3393
9-7773
0-2023
9 3837
9-8204
0-2441
9-4280
9-8633
0-2858
9-4721
9-9062
3273
9-5161
9-9489
0-3687
9-5600
9 9914
4100
9-6037
*0-0338
4512
9 6473
*0-0761
0-4922
-0441
0428
0415
61
65
66
22 0-5332
0-9359
1-3267
0-5740
0-9755
1-3651
6147
1 0151
1-4034
6552
1 0544
1-4416
0-6957
1-0937
1-4797
0-7360
1-1328
1-5177
0-7762
1-1718
1-5555
0-8163
1-2107
1-5933
0-8563
1-2495
1 6309
0-8962
1-2881
1-6684
-0403
0391
■0379
67
68
69
22 1-7059
2 0742
2-4322
1-7432
2 1105
2-4675
1-7804
2 1466
2-5027
1 8175
2-1827
2-5377
1-8545
2-2186
2-5727
1-8914
2-2545
2-6076
1-9281
2-2902
2-6424
1-9648
2-3259
2-6771
2-0014
2-3614
2 7117
2-0378
2-3969
2-7462
0368
0358
0348
70
71
72
22 2-7806
3-1196
3-4492
2-8150
3 1530
3-4816
2-8492
3 1863
3 5140
2-8833
3-2195
3-5462
2-9174
3-2526
3-5784
2-9513
3-2856
3 6105
2-9852
3-3185
3 6424
3 0189
3-3513
3-6743
3 0526
3 3840
3 7061
3-0862
3-4167
3-7378
0339
-0330
-0320
73
71
75
22 3 7694
4 0804
4-3828
3-8009
4-1110
4 4125
3-8323
4 1416
4-4422
3-8636
4 1720
4-4719
3-8949
4-2024
4-5014
3-9260
4-2326
4-5308
3-9571
4-2628
4-5602
3-9881
4-2929
4-5895
4-0189
4 3230
4 6187
4-0497
4-3529
4-6478
0311
-0302
-0294
76
77
78
22 4-6769
1 4-9624
5-2394
4-7058
4-9905
6-2666
4-7347
5-0185
5-2937
4-7635
5 0464
5 3208
4-7922
5-0742
5-3478
4-8208
5-1020
5-3747
4-8493
5 ■ 129G
5-4015
4-8777
5 • 1572
5-4282
4-9060
5 1847
5-4549
4 9343
5-2121
5 4814
-0286
•0277
-0268
79
80
81
22 5-5079
5-7685
6 0214
5-5343
5 7941
6-0463
5-5606
5-8197
6 0711
5-5869
5 - 8452
6-0959
5-6130
5-8706
6-1205
6-6391
5-8959
6-1451
5-6652
5-9212
6-1696
5-6911
5-9463
6-1941
5-7170
5-9714
6-2184
5-7428
5-9965
6-2427
-0261
-0253
-0245
82
83
84
22 6-2669
6-5044
6-7337
6-2910
6-5277
6-7562
6 3151
6-5509
6-7786
6-3390
6 5740
6-8009
6-3629
6-5971
6-8232
6-3867
6 6201
6-8454
6-4104
6 6430
6-8675
6-4340
6 6658
6-8895
6-4576
6-6885
6-9114
6 4810
6-7111
6 9333
0237
0229
-0221
85
86
22 6-9551
■7- 1688
7-3752
6-9768
7-1898
7-3954
6-9984
7-2107
7 -U5G
7 0200
7 ■ 2:315
7-43J7
7 -0415
7-2522
7-4358
7-0629
7-2729
7-4757
7 -0842
7-2935
7-4956
7-1055
7 3140
7-5155
7 -1267
7-3345
7 5353
7-1478
7-3549
-0214
-0206
0199
XX. — EXTERIOR BALLISTICS.
55
Table II. — Continued.
Time and Velocity Table, Gt — r^,
22 7
7
7
22 8
22 8
22 9
9
9
22 9
22 9
23
23
23
23
23
23 1
•1
1
23 1
1
1
23 1
1
1
23 1
1
1
23 1
1
1
5746
7677
9544
1346
3090
4778
6411
7994
9528
1014
2454
3851
5207
6522
7796
9024
0177
1226
2170
3031
3835
4593
5314
6668
7311
8545
9142
9720
0283
0832
1367
3381
3855
4318
4771
5214
5647
6071
6486
6893
23 1 7291
1-7682
1-8066
5942
7866
9727
1523
3261
4943
6572
8150
9678
1160
2596
5340
6651
7921
9144
0287
1325
3114
3913
4667
5384
6071
6733
7374
7997
8605
9200
9777
0338
0886
1420
1941
2449
2945
3429
3902
4364
4816
5257
5690
6113
6527
6933
7331
7721
8104
6137
8055
1699
3432
5109
6732
8305
1306
2737
4126
5473
6780
8046
9262
0396
1423
4740
5454
6139
6798
7437
8059
8665
9259
0394
0940
1473
1992
2499
2994
3477
3948
4410
4860
5301
5732
6155
6568
7370
7760
8142
2347
3196
6332
8244
0091
1875
3602
5273
8459
9978
1451
2878
4262
5606
6C08
8170
0504
1520
2435
3278
4067
4813
5524
6206
6863
7500
8120
8726
9317
0449
0934
1525
2549
3043
3524
3995
4455
4905
5345
5775
6196
6609
7013
7410
7798
8179
6526
8431
0272
2050
3772
5437
7051
8613
0128
1595
3018
4398
5738
7036
8294
9496
0610
1615
2522
3359
4143
4885
5593
7563
8181
8787
9375
9947
0504
1048
1578
1-2095
1-2599
1 3091
3572
4041
4501
4949
5388
5818
7449
7837
8217
6719
sees.
7-
0452 j 8
2225 ! 8
3941 8
5601
7209
8767
0276
1740 ' 9
3158 ! 9
4534 9
7164
8417
9612
071G
1710
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3439
4219
4958
5662
6339
7625
8242
8847
9433
0003
0559
1101
1630
2146
2649
3140
3619
4088
4546
7875
8255
6912
0632
4109
5764
7367
8920
0425
1884
3298
4670
6001
7291
8540
9727
0820
1804
2694
3520
4295
5731
6405
7056
7688
9490
0059
0614
1154
1682
2196
2698
4134
4591
5475
5902
6321
6731
7133
7527
7913
8292
7
9
9
sees.
7-7104
7-8991
8-0812
sees.
7 7295
7 9176
8-0990
sees.
7 7486
7 9360
8 1168
8-2573
8 4277
8 5927
8 2746
8-4445
8-6089
8-2918
8-4611
8 6250
8-7525
8 9073
9-0573
8-7682
8-9225
9 0720
8-7838
8 9376
9 0867
9 2027
9-3437
9-4805
9-2170
9 3575
9-4939
9 2312
9 3713
9 5073
9-6132
9-7418
9-8662
9-6262
9-7544
9-8783
9-6392
9 7670
9 8904
9-9841
0923
0-1897
9-9954
1025
1988
*0 0066
1126
0-2079
0-2780
3599
4370
0-2864
0-3678
0-4445
2948
3757
4519
0-5101
5800
6471
0-5172
0-5868
6537
0-5243
5936
6603
0-7120
7750
0-8364
0-7184
7812
8424
0-7248
0-7874
0-8484
0-8965
0-9648
1-0115
9024
9605
1-0171
9083
9663
1 0227
10669
1-1208
11734
1 0723
1-1261
1 1786
10778
1-1314
1-1838
1-2247
1-2748
1 3237
1-2298
1 2797
1-3285
1-2348
1-2847
1 3333
1 3714
1-4180
1-4636
1-3761
1 4226
1-4681
1-3808
1-4272
1-4726
1-6082
1-5518
1-5945
1-5126
1-5561
1-5987
1 5170
1 5604
1-6029
1-6362
1-6772
1-7173
1 6404
1-6812
1 7212
1 6445
1-6852
1 7252
1 7566
1-7952
1 8330
1 7605
1-7990
1-8367
1-7644
1-8028
1-8405
m
X5t. — EXTERIOR BALLISTICS.
Table II. — Continued.
Time and Velocity Table, Ct = r
23 1
1
23 2
2
2
23 2
2
2
23 2
2
23 2
2
2
23 2
2
2
23 2
2
2
23 2
2
2
23 2
2
2
23 2
2
2
23 2
23 2
2
2
23 2
23 3
3
3
23
8442
8812
9175
9532
9883
0228
0569
0904
1234
2197
2509
2818
3123
3424
3722
4016
4308
4597
4882
5165
5444
5721
5994
62G5
6533
6798
7061
7320
7577
7832
8084
8333
8580
8824
9065
9304
9541
9776
0008
0237
0465
0690
0913
1134
1353
1569
•8479
•8848
•9211
!•{
1^{
1 <
•9567
•9918
•0263
1^{
!•'
2 (
0602
•0937
•1267
2 (
2(
2 ]
•1591
•1912
•2228
2 ]
2 ]
2 5
•2540
•2849
•3153
2-'
2'
2-
•3454
•3751
•4046
2-
2-
2
•4337
■4625
•4911
2-
2-
2-
•5193
•5472
•5748
2-
2-
2-
•6022
•6292
•6560
2-
2-
2
•6825
•7087
7346
2-
2-
2-
•7603
•7857
•8109
2
2-
2-
•8358
•8604
•8848
2
2-
2-
•9089
•9328
•9565
2-
2-
2-
•9799
J 0031
5 0260
2-
3-
3-
r0488
J 0713
{•0935
3
3^
3-
$1156
$1375
J 1591
3
3
3-
•8517
•8885
•9247
•9602
•9952
•0297
•0636
•0970
•1299
•1624
•1944
•2260
•2571
■2879
•3484
•3781
•4075
•4366
•4654
•4939
•5221
•5500
•5776
•6049
•6319
•6851
•7113
•7372
•7628
•7882
•8134
•8629
•8872
•9113
•9352
•9822
0054
0510
•0735
■0958
1178
1396
•1613
8554
8921
9282
9638
9987
0331
0670
1003
1332
1656
1975
2291
2602
2910
3214
3514
3810
4104
4395
4683
4967
5249
5528
6076
6346
6877
7139
7398
7654
7908
8159
8407
8653
2 9137
2
2 9612
2-9845
3 0077
3 0306
3 0533
3 0757
3 1200
3 1418
3 1634
8591
8958
9318
9673
0022
0365
0703
1036
1364
1688
2007
2322
2633
2940
3244
3543
3840
4133
4424
4711
4996
5277
5555
5831
6373
6640
7165
7423
7679
7933
8184
8432
8678
8921
9161
9399
9635
0100
0329
0555
0780
1002
1222
1440
1656
8628
8994
9354
9708
0056
0399
0737
1069
1397
1720
2039
2354
2664
2971
3274
3573
3869
4162
4453
4740
5024
5305
5583
5858
6130
6400
6666
7191
7449
7705
7958
8209
8457
8702
9185
9423
9659
9892
0123
0351
0578
0802
1024
1244
1461
1677
8665
9030
9743
0091
0433
0770
1102
1430
1752
2071
2385
2695
3001
3304
3899
4192
4481
4768
5052
5333
5611
6157
6426
6956
7217
7475
7730
7983
8234
8481
8726
9209
9447
9682
9915
0146
0374
0600
0824
1045
1266
1483
1698
8702
9067
9425
9778
0125
0467
1135
1462
1784
2102
2416
2726
3032
3928
4221
4510
4797
5080
5361
5638
5913
6184
6453
6719
6982
7243
7500
7756
8008
8258
8506
8751
9470
9705
9938
0169
0397
0623
0847
1068
1287
1505
1720
8738
9103
9461
9813
0160
0501
1168
1494
1816
2134
2447
2757
3062
3958
4250
4539
4825
5108
5666
5940
6211
6480
6745
7008
7268
7526
7781
8034
8283
8531
8775
9017
9257
9494
9729
9961
0192
0420
0645
0869
1090
1309
1526
1741
8775
9139
•9848
0194
0535
0870
1201
1527
1848
2165
2478
2787
3093
3394
3692
3987
4279
4568
4854
5137
5416
5693
5967
6238
6506
6772
7034
7294
7552
7806
8059
8308
8555
8799
9041
•9281
•9518
•9752
0215
0442
0668
0891
1112
XX. — EXTERIOR BALLISTICS.
57
Table II. — Continued.
Time and Velocity Table, Ct = r^, — r^„
V.
1
2
3
4
5
6
7
8
9
Diff.
f.R.
184
185
18G
sees.
23 3 1784
3 1997
3 2207
Bees.
3 1805
3-2018
3-2228
sees.
3 ■ 1827
3 2039
3-2249
g
3
3
3
ecs.
1848
2060
2270
sees.
3-1869
3-2081
3-2291
s
3
3
3
eca.
1891
2102
2312
sees.
3-1012
3-2123
3-2333
sees.
3 1033
3-2144
3-2353
8
3
3
3
ecs.
1954
2165
2374
sees.
3-1975
3-2186
3-2395
+
•0021
-C021
0021
187
188
139
23 3 2416
3-2623
3-2828
3-2437
3-2643
3-2848
3 2457
3-2664
3-2869
3
3
3
2478
2683
2889
3-2499
3-2705
3-2909
3
3
3
2520
2726
2930
3 2540
3-2746
3-2950
3-2561
3 2767
3-2970
3
3
3
2582
2787
2091
3-2602
3-2803
3-3011
-0021
-0021
0020
100
191
102
23 3-3031
3-3233
3-3432
3-3051
3-3253
3-3452
3-3072
3-3273
3 3472
3
3
3
3092
3293
3492
3-3112
3-3313
3-3511
3
3
3
3132
3333
3531
3-3152
3-3353
3-3551
3-3172
3 3372
3-3571
8
3
3
3102
3302
3500
3-3212
3-3412
3-3G10
-0020
-0020
-0020
193
104
105
23 3-3630
3-3825
3 4019
3-3649
3 3845
3 4038
3-3669
3-3864
3-4057
3
3
3
3689
3884
4077
3-3708
3 3903
3 4096
3
3
3
3728
3922
4115
3-3747
3-3942
3 4134
3-3767
3-3061
3 4153
3
3
3
3786
3080
4172
3-3806
3 4000
3-4192
-0020
0019
0019
IOC
107
108
23 3 4211
3 4400
3-4588
3-4230
3-4419
3 4606
3-4240
3-4438
3-4625
3
3
3
4268
4457
4644
3-4287
3 4476
3-4662
3
3
3
4306
4494
4681
3-4325
3-4513
3-4699
3 4344
3-4532
3-4718
3
3
3
4362
4550
4736
8-4381
3-45C9
3-4755
0019
0019
0019
100
200
201
23 3 4773
3-4956
3-5137
3 4791
3-4074
3 5155
3-4810
3-4002
3-5172
3
3
3
4828
5010
5190
3-4846
3-5028
3 5208
3
3
3
4865
5047
5226
3-4883
3-5065
3 5244
3-4901
8-5083
3-5262
3
3
3
4920
5101
5280
3-4938
3-5119
3-5297
-0018
0018
0018
202
203
204
23 3-5315
3-5402
3-5666
3-5333
3-5500
3-5683
3-5351
3-5527
3-5700
3
3
3
5368
5544
5717
3-5386
3-5561
3 5735
3
3
3
5404
5579
5752
3-5421
3-5596
3-5769
3-5439
3-5614
3-5786
3
3
3
5456
5631
5803
8-5474
3-5648
3 5820
0018
•0017
0017
205
208
207
23 3-5837
3 6007
3-6174
3-5854
3-6024
3 6191
3-5871
3-6040
3-6207
3
3
3
5888
6057
6224
3 5905
3-6074
3 6240
3
3
3
5922
6091
6257
3-5939
3-6107
3-6273
3 5956
3-6124
3-6290
8
3
3
5973
6141
6306
3-5990
3-6157
3 6323
0017
-0017
-0016
203
2O0
210
23 3 6339
3 6502
3-6662
3-6355
3-6518
3 -6078
3-6372
3-6534
3-6694
3
3
3
6388
6550
6710
3 6404
3-6566
3-6726
3
3
3
6420
6582
6741
3-6437
3-6598
3-6757
3-6453
3-6614
3-6773
3
3
3
6469
6630
6789
8 6485
3-6646
3 6805
-0016
0016
0016
211
212
213
23 3-6820
3-6977
3-7131
3 6836
3-6902
3-7146
3-6852
3-7008
3-7162
3
3
3
6867
7023
7177
3-6883
3-7039
3-7192
3
3
3
6899
7054
7207
3-6914
3 7070
3 7223
3-6930
3-7085
3-7238
3
3
3
6946
7100
7253
8-6961
3-7116
3-7268
0016
•0015
0015
214
215
216
23 3-7283
3-7434
3-7582
3-7298
3 7448
3-7597
3 7313
3 -7463
3 7612
3
3
3
7329
7478
7626
3 7344
3-7493
3 7641
3
3
3
7359
7508
7656
3-7374
3-7523
3 7670
3-7389
3-7538
3-7685
3
3
3
7404
7552
7700
3-7419
3-7567
3-7714
0015
0015
-0015
217
218
210
23 3 7729
3-7874
3-8016
3 7743
3 7888
3 8031
3-7758
3 7002
3 8045
3
3
3
7772
7917
8059
3-7787
3-7931
3 8073
3
3
3
7801
7945
8087
3-7816
3-79G0
3-8101
3-7830
3-7974
3 8115
3
3
3
7845
7988
8129
3-7859
3 8002
3-8144
0014
OOU
0014
220
221
222
23 3-8158
3-8297
3 8435
3-8372
3 8311
3 8448
3 8186
3-8325
3 8462
3
3
3
8200
8338
8476
8-8214
3 8352
3 8489
3
3
3
8227
8366
8503
3-8241
3-8380
3 8517
3-8255
3 8394
3 8530
3
3
8269
8407
8544
8 8283
3-8421
3-8557
0014
0014
0014
223
224
225
23 3-8571
3-8705
3-8838
3-8584
3-8718
3-8851
3 8508
3-8732
3-8864
3
3
3
8611
8745
8877
3-8625
3-8758
3-8890
3
3
3
8638
8772
8903
3-8651
3-8785
3 8916
3-8665
3-8798
3-8930
3
3
3
8678
8811
8943
8-8692
3 8824
3-8956
i ooia
0013
-0013
226
227
228
23 3 8969
3 00'^«
3-922G
3-8982
3-9111
3 92u9
3-8995
3 9124
3-9252
3
3
3
-9008
-9137
9264
3-9021
3-9150
3-9277
3
3
3
9034
9162
9290
3-9047
3-9175
3 y..03
3-9059
3-91R8
3 9315
3
3
3
9072
9201
-9323
3-9085
3-9214
3 9341
001&
0013
•0013
229
230
23 3-9353
3 9470
3-9366
3-9i92
3-937S
3- 0:01
3
-9301
-9517
3 9401
3 -2029
3
9*15
' 3-9429
3-9554
3-9441
3-9507
8
3
-9454
9579
3-9467
3-9592
0013
0013
58
XX. EXTERIOR BALLISTICS.
Table III
Distance and Velocity Table, Cs = c^ — (7^/,.
feet.
2 5008
5424
5827
2 6219
6601
6972
2 7335
7688
8034
2 8373
8704
9029
2 9347
9659
9966
3 0267
0.563
. 0854
3 1140
1423
1701
3 1076
2247
- 2514
3 2777
3037
3292
3 3544
3793
4038
3 4280
4519
4754
3 4986
5215
5440
3 5662
5S80
6094
3 6305
6512
6716
3 6916
7111
7303
3 74nO
7672
7850
feet.
5050 2
5464-9
5867-3
6258
6638
7009
7370
7723
8068
8406
8737
9061
9690
0297
0592
1169
1451
1729
7
2274
2540 8
3318
3569
3818
4062
4304
4543
4777
5009
5237
5462
5684
5902
6116
6326
6533
7
5
1
1
4
1
6736 3
6935 7
7131
7322
7^0'^ -5
7690-5
7868-2
feet.
5092
5505
5903
6296
6676
7046
7406
7758
8103
8439
8769
9093
9410
9721
0027
0327
0622
0912
1197
1479
1757
2031
2301
2567
2829
3038
3343
3594
3842
4087
4328
4566
4801
5032
52G0
5484
5706
5923
6137
6347
6553
6756
6955
7150
7340
7526
7708
7885
feet.
5134
5546
5946
6335
6713
7082
7442
7793
8137
8473
8802
9125
9441
9752
^0057
0357
0651
0940
1226
1507
1784
2058
2327
2855
3114
3619
3867
4111
4352
4590
5055
5282
5507
5728
5945
6158
6368
6574
6776
6975
7169
7359
7.^45
7726
7903
feet.
5176
5586
5985
' 6373
6751
I 7118
I
: 7477
7828
1 8170
8835
9157
6 9472
2 9783
3 *0087
0386
0680
9 , 0969
1254
1535
1812
2354
2020
28S1
3139
3394
3644
3891
4135
4376
4613
4847
5078
5305
5529
5749
5966
6179
6594
6796
6994
7188
7378
3 7563
4 7744
3 ' 7920
I
feet.
5217
5627
6025
6411
6788
7155
7513
7862
8204
8539
8867
9189
9504
9813
mi7
0416
0709
0998
1282
1563
1839
2112
2381
2646
2907
3165
3419
3669
3916
4159
4400
4637
4871
5101
5328
5551
5771
5988
6200
6409
6614
6816
7014
7207
7397
7581
7762
7938
feet.
5259
5667
6064
6449
6825
7191
7548
7897
8572
8900
9220
9535
9844
"^0147
0445
0738
1026
1310
1590
1867
2139
2407
2672
2933
3191
3444
3694
3940
4184
4424
4660
4894
5124
5350
5573
5793
6009
6221
6430
6635
7033
7227
7415
7600
7779
7955
feet.
5300
5707
6103
6487
6862
7227
7583
7931
8272
8932
9252
9566
9874
'^0177
0475
0767
1055
1339
1618
1894
2166
2434
2959
3216
3469
3719
3965
4208
5815
6030
6242
64.50
6655
6856
7053
7246
7434
7618
7797
7973
4448 -0
4684-4
4917-4
5146 9
5373
5595
feet.
5341
5747
6142
6525
6899
7263
7618
7966
8305
8964
9284
9597
9905
'0207
0504
0796
1367
1646
1921
2193
2461
2725
2985-4
3242
3494 7
3743
3989
4232
4471
4707
4940
5169
5395
5617
5837
6052
6263
6471
6675
6876
7072
7265
7453
7636
7815
7990
feet.
5383
5787 8
6181
6563-6
6936 1
7299-2
7653-9
8000
8671
8996
9315
9628
9935
^0237
0534
0825
1112
1395
1674
1949
2220
2487
2751
3011
3267
3519
3768
4014
4256
4495
4731
4963
, 5192
! 5417
5640
5858-7
6073-6
6284 6
6492
7092
7284
7471
76.54
7833
8007
XX — EXTERIOR BALLISTICS.
Table III. — Continued.
Distance and Velocity Table, Cs = o-^, — cr^,,.
V.
1
2
3
4
6
6
7
8
9
Dim
88
89
90
feet.
3 8024-8
8195
8361-5
feet.
8042
8211-9
8377-9
feet.
8059 2
8228-6
8394-3
feet.
8076.3
8245 4
8410-7
feet.
8093-4
8262-1
8427-0
feet.
8110-4
8278-7
8443-3
feet.
8127-4
8295-4
8459-6
feet.
8144-4
8312-0
8475-8
feet.
8161 3
8328-5
8492-0
feet.
8178-2
8345-0
8508-2
+
17-0
16 6
16-3
91
92
93
3 8524-3
8683-5
8839-4
8540 4
8699-3
8854-8
8556-4
8715-0
8870-2
8572-4
8730-7
8885-5
8588-4
8746-3
8900-8
8604-3
8761-9
8916-1
8620-3
8777-5
8931-3
8636-1
8793-0
8946-5
8652-0
8808-5
8961-7
8667-8
8824-0
8976-8
15 9
15-6
15 3
94
95
96
3 8991-9
9141 2
9287 4
9007-0
9156
9301-9
9022-0
9170-7
9316 3
9037-0
9185-4
9330-7
9052-0
9200 1
9345
9066-9
9214-7
9359-4
9081-9
9229-3
9373-7
9096-7
9243-9
9387-9
9111-6
9258 4
9402-2
9126-4
9272-9
9416-4
15
14-6
14-3
97
98
99
3 9430 6
9570 8
9708-3
9444-7
9584-7
9721-9
9458 9
9598-6
9735-4
9473-0
9612-4
9749-0
9487-0
9626 1
9762-5
9.501-1
9639-9
9775-9
9.515-1
96.53-6
9789-4
9529 1
9667-3
9802-8
9543-0
9681-0
9816-2
9557-0
9604-6
9829-6
14
13-7
13-5
100
101
102
3 9842 9
9975
4 0104 3
9856 3
9988 1
0117 1
9869-6
*0001-1
0129 8
9882-9
*()014-1
0142-5
9896-1
*0027-l
0155-2
9909-3
:*0040-0
0167-8
9922-5
*00.52-9
0180-4
9935-3
*0065-8
0192 9
9948 8
*0078-7
0-205 4
9961-9
*009l-5
0217-8
13-2
12-9
12-6
103
104
105
4 0230-1
0349 4
0459-2
0242 4
0360-8
0469 6
0254-6
0372-2
0479-9
0266-8
0383-4
0490-0
0278-8
0394-5
0500-1
0290-8
0405-6
0510 1
0302-7
0416-5
0520
0314 5
0427-3
0529-8
0326-2
0438-1
0539 5
0337-8
0448-7
0549-2
11 9
11-0
9-9
106
107
108
4 0558 7
0650 5
0736-8
0568-2
0659-3
0745 2
0577 6
0668 1
0753 6
0.586-9
0676-9
0761-9
0596 2
0685-6
0770-2
0605-4
0G94-2
0778-4
0614-5
0702-8
0786-6
0623-6
0711-4
0794-8
0632-6
0719-9
0802-9
0641-6
0728-4
0811-0
9 2
8 6
8-2
109 '
110
111
4 0819
0897-9
0974-2
0827-1
0905 7
0981 6
0835
0913-4
0989 1
0843-0
0921-1
0996 6
0850-9
0928-7
1004-0
0858-9
0936-4
1011-4
0866-7
0944-0
1018-8
0874-6
09.51-5
1026 2
0882-4
0959 1
1033-5
089(r
0966
1040
2
6
9
7-9
7-6
7-4
112
113
lU
4 1048 2
1120 5
1191 4
1055-5
1127-6
1198-4
1062-8
1134-8
1205-4
1070
1141 9
1212 4
1077-3
1149-0
1219-4
1084-5
1156-1
1226-4
1091-7
1163 2
1233 3
1099
1170 2
1240 3
1106-1
1177-3
1247-2
1113
1184
1254
3
4
1
7-2
71
6 9
115
116
117 1
4 1261
1329-5
1396 8
1267-9
1336 3
1403-5
1274-8
1343-1
1410 1
1281-7
1349 8
1416-8
1288-6
1356 6
1423-4
1295-4
1363-3
1430
1302-3
1370
1436-6
1309 1
1376-7
1443-2
1315-9
1383-4
1449-8
1322
1390
1456
7
1
4
6 8
6 7
66
118
119 i
120
4 1462 9
1528-0
1591 9
1469 5
1534-4
1598-3
1476-0
1540 9
1604-6
1482 6
1547-3
1610-9
1489-1
1553-7
1617-2
1495-6
1.560-1
1623-5
1502 1
1566-5
1629-8
1508 6
1572-9
1636-1
1515-1
1,579-2
1642-3
1521
1585
1648
5
6
6
6 5
6-4
6 3
121
122
123
4 1654-8
1716 7
1777-5
1661 1
1722-8
1783 6
l«67-3
1728-8
1789-6
1673-5
1735
1795-6
1679-7
1741 1
1801 6
1685-9
1747-2
1807-6
1692-1
1753 3
1813-6
1698-2
1759-4
1819-6
1704-4
1765 4
1825 6
1710
1771
1831
5
5
5
6-2
6-1
6
124
125 1
126
4 1837 5
1896 5
1954-6
1843 4
1902 3
1960 4
1849-4
1908-2
1966-1
1855-3
1914
1971-9
1861-2
1919-8
1977 6
1867-1
1925-6
1983 3
1873-0
1931-5
1989-0
1878-9
1937-3
1994-8
1884-8
1943
2000 5
1890
1948
2006
6
8
2
5 9
5 8
5-7
127
128
129
4 2011-8
2068-3
21-23-9
2017-5
2073-9
2129-4
2023-2
2079 5
2135
2028-9
2085-0
2140 5
2034-5
2090-6
2146-0
2040-2
2096-2
2151-5
2045-8
2101 8
2157-0
2051-4
2107-3
2162-4
2057
2112-9
2167-9
2062
2118
2173
7
4
4
5-6
5-6
5-5
130
131
132
4 2178-8
2233
2286 4
2184-3
2238-4
2291-8
2189-7
2243-7
2297-1
2195-1
2249-1
2302-4
2200-6
2254-5
2307-6
2206
22.59-8
2312 9
2211-4
2265-1
2318-2
2216-8
2270-5
2323 5
2222-2
2275-8
2328-7
2227
2281
2334
6
1
5-4
5 3
53
133
134
135
4 2339-2
2391-4
2443
2344-5
2396 6
2448-1
2349-7
2401 8
2453-2
2355
2406 9
2458-3
2360 2
2412 1
2463 4
2365-4
2417-3
2468-5
2370-6
2422-4
2473-6
2375-8
2427-6
2478-7
2381-0
2432-7
2483-8
2386
2437
2488
2
8
9
6-2
5-2
5-1
60
XX. — EXTERIOR BALLISTICS.
Table III. — Continued.
Distance and Yelocity Table, Gs = cr^,
V.
1
2
3
4
5
6
7
8
9
Diff.
f.s.
136
137
138
feet.
4 2493-9
2544 4
2594-3
feet.
2499
2549-4
2599-2
feet.
2504 1
2554-4
2604-2
feet.
2509-1
2559-4
2609 1
feet.
2514-2
2564-4
2614-1
feet.
2519-2
2569-4
2619
feet
2524-
2574-
2624-
3
4
feet.
2529-3
2579 4
2628-9
feet.
2534-3
2584-3
2633-8
feet.
2539-4
2589-3
2638-8
+
5
5
4 9
139
110
141
4 2643-7
2692-6
2741-2
2648-6
2697-5
2746-0
2653-5
2702-4
2750-8
2658-4
2707-2
2755-7
2663-3
2712-1
2760-5
2668-2
2717
2765-3
2673
2721
2770
1
8
1
2678-0
2726-7
2774-9
2682-9
2731-5
2779-7
2687-8
2736-3
2784-5
4-9
4-9
4-8
142
143
144
4 2789-3
2837-1
2884-4
2794 1
2841-8
2889 1
2798-9
2846-6
2893-8
2803-7
2851-3
2898-6
2808-5
2856-0
2903-3
2813-2
2860-8
2908-0
2818
2865
2912
5
7
2822-8
2870-2
2917-4
2827-5
2875-0
2922-1
2832-3
2879-7
2926-7
4-8
4-7
4-7
145
146
147
4 2931-4
2978-1
3024-5
2936 1
2982-8
3029 1
2940-8
2987-4
3033-7
2945-5
2992-1
3038-4
2950 1
2996-7
3043-0
2954-8
3001-3
3047 6
2959
3006
3052
5
2
2964-1
3010-6
3056-8
2968-8
3015-2
3061-4
2973-5
3019-9
3066-0
4 7
4 6
4-6
148
149
150
4 3070-6
3116 4
3162-0
3075-2
3121
3166 5
3079 8
3125-6
3171
3084-4
3130 1
3175 6
3089
3134-7
3180 1
3093-5
3139-2
8184-6
3098
3143
3189
1
8
2
3102-7
3148-3
3193-7
3107-3
3152-9
3198-2
3111-8
3157-4
3202-7
4-6
4 6
4-5
151
152
153
i 3207 2
3252 3
3297-2
3211 • 8
3256-8
3301-7
3216-3
3261-3
3306-2
3220-8
3265-8
3310-6
3225-3
3270-3
3315 1
3229-8
3274-8
3319-6
3234
3279
3324
3
3
1
3238-8
3283-8
3328-5
3243-3
3288-3
3333-0
3247-8
3292-8
3337-5
4-5
4 5
4 5
154
155
156
4 3342-0
3386-5
3430 9
3346-4
3391-0
3435-3
3350 9
3395-4
3439-8
3355-3
3399-9
3444-2
3359-8
3404 3
3448-6
3364-3
3408-7
3453
3368
3413
3457
7
2
4
3373-2
3417-6
3461-9
3377 6
3422
3466-3
3382-1
3426-5
3470-7
4-5
4-4
4-4
157
158
159
4 3475-1
3519-1
3563-0
3479-5
3523-5
3567-3
3483-9
3527-9
3571-7
3488-3
3532 3
3576-1
3492-7
3536-7
3580-4
3497 1
3541 1
3584-8
3501
3545
3589
5
4
1
3505-9
3549-8
3593-5
3510 3
3554 2
3597-9
3514-7
3558-6
3602 2
4-4
4-4
4-4
160
161
162
4 3606 6
3650-0
3693-3
3610-9
3654-3
3697 6
3615-3
3G58-7
3701-9
3619-6
3663
3706-1
3624-0
3667-3
3710-5
3628-3
3671-6
3714 8
3632
3676
3719
6
1
3637
3680-3
3723-4
3641-3
3684-6
3727-7
3645-7
3688-9
3732-0
4-3
4-3
4-3
163
164
165
4 3736-3
3779-2
3821-9
3740-6
3783-5
3826-2
3744-9
3787-8
3830-4
3749 2
3792
3834-7
3753-5
3796-3
3838-9
3757-8
3800-6
3843-2
3762
3804
3847
1
9
4
3766-4
3809-1
3851-7
3770 6
3813-4
3855-9
3774-9
3817-6
3860-2
4 3
4-3
4-3
166
167
168
4 3864-4
3906-8
3949
3868-7
3911-0
3953 2
3872-9
3915-2
3957-4
3877-2
3919-5
3961-6
3881-4
3923-7
3965-8
3885-6
3927-9
3970-0
3889
3932
3974
9
1
2
3894-1
3936 3
3978-4
3898-3
3940 5
3982-6
3902-5
3944-7
3986-7
4-2
4-2
4 2
169
170
171
4 3990-9
4032-7
407i 3
3995-1
4036 9
4078-5
3999 3
40111
4082-6
4003-5
4045-2
4086-8
4007-7
4049-4
4090-9
4011-9
4053-6
4095-1
4016
4057
4099
7
2
4020-2
4061-9
4103 3
4024-4
4066-0
4107-5
4028-6
4070-2
4111-6
4-2
4 2
4 1
172
173
174
4 4115-7
4157
4198
4119-9
4161-1
4202 1
4124-0
4165-2
4206-2
4128-1
4169-3
4210 3
4132-3
4173-4
4214-4
4136-4
4177-5
4218-5
4140
4181
4222
5
6
6
4144-6
4185-7
4226-7
4148-7
4189-8
4230-8
4152-9
4193-9
4234-8
4-1
4 1
4 1
175
176
177
4 4238 9
4279 6
4320 2
4243
4283-7
4324-2
4247-1
4287-8
4328-3
4251-2
4291-8
4332 -3
4255-3
4295-9
4336-4
4259-3
4300-0
4340-4
4263
4304
4344
-4
-4
4267-5
4308-8
4348 5
4271-5
4312-1
4352-5
4275-6
4316 1
4356-5
4-1
41
4-0
178
179
180
4 4360-5
4100 7
4440-8
4364-6
4404-7
4444-7
4368-6
4408 8
4448-7
4372-0
4412-8
4452-7
4376-6
4416 8
4456-7
4380-7
4420-8
4460-7
4384
4424
4464
-7
-8
7
4388-7
4428-8
4468-7
4392 7
4432 8
4472-6
4396-7
4436-8
4476-6
40
4
40
181
182
183
4 4480 6
4520-3
4559-8
4484-6
4524-2
4563-7
4488 5
4528-2
4567-7
4492 5
4532-2
4571-6
4496-5
4536 1
4575-6
4500 5
4540-1
4579-5
4501
4544
4583
•4
4
4. '08 -4
4518
4587-4
4512-4
4551-9
4591-3
4516-3
4555 9
4595-2
4-0
40
3-9
XX. — EXTERIOR BALLISTICS.
61
Table III . — Continued.
Distance and Velocity Table, Cs — a^' — cr^„.
V.
1
2
3
4
5
6
7
8
9
Diffi
f.s.
184
185 !
186
feet.
4 4599-2
4638-4
4677-4
feet.
4603-1
4642-3
4681-3
feel
4607
4646
4685
2
2
feet
4610
4650
4689
9
feet.
4614-9
4654
4693-0
feel
4618
4657
4696
8
9
9
feet.
4622-7
4661-8
4700 8
feel
4626
4665
4704
6
7
6
feet.
4630-5
4669-6
4708-5
feet.
4634-4
4673 5
4712-4
+
3-9
3-9
3-9
187
188 '
189
4 4716 3
4755
4793 7
4720-2
4758-9
4797-5
4724
4762
4801
1
8
4
4727
4766
4805
4731-8
4770 5
4809-1
4735
4774
4812
7
4
9
4739-6
4778-2
4816-8
4743
4782
4820
4
1
6
4747-3
4786-0
4824-5
4751-2
4789-8
4828-3
3 9
3 9
3 8
190
191 i
192 j
4 4832-2
4870-5
4908-7
4836
4874-3
4912 5
4839
4878
4916
8
1
3
4843
4882
4920
4847-5
4885-8
4923-9
4861
4889
4927
4
6
7
4855-2
4893 4
4931-5
4859
4897
4935
3
3
4862-8
4901-1
4939-1
4866-7
4904-9
4942-9
3 8
3 8
3 8
193 i
194
195
4 4946-7
4984-5
5022 2
4950-5
4988-3
5025 9
4954
4992
5029
3
1
7
4958
4995
5033
4961-9
4999 6
6037-2
4965
5003
5040
7
4
9
4969-4
5007-1
5044-7
4973
5010
5048
2
9
4
4977-0
5014 7
5052-1
4980-7
5018-4
5055-9
3-8
3-8
3 7
196
197
198 ,
4 5059-6
5096-9
5133-9
5063-4
5100 6
6137-5
5067
5104
6141
1
3
2
5070
5108
5144
8
9
5074-6
5111-7
5148 6
5078
5115
5152
3
4
3
5082-0
5119 1
5150-0
5085
5122
5159
7
8
6
6089-4
5126-5
5163-3
5093 1
5130 2
6166 9
3-7
3-7
3 7
199
200
201
4 5170-6
5207-1
5243-3
5174-3
5210-7
6246-9
5177
5214
5250
9
3
5
5181
5218
5254
6
1
5185-2
5221-6
5257-7
5188
5225
5261
9
2
3
5192-5
5228-8
6264-9
5196
5232
5268
2
5
5
5199-8
5236-1
5272-1
5203-4
5239-7
5275 7
3 6
3 6
3 6
202
203
204
4 5279 2
631 i 9
6360-3
5282 8
6318-5
5353-8
5286
5322
5357
4
3
5290
5325
5360
6
9
5293-0
5329-1
6364-4
5297
5332
5367
2
7
9
5300-7
5336 2
6371-4
5304
5339
5374
3
7
9
5307-8
5343-3
5378-4
5311 4
5346 8
5391 9
3 6
3 5
3-5
205
206
207
4 5385-4
6420-2
5454-7
5388 9
5423-7
6458-1
5392
5427
5461
4
1
6
5395
5430
5465
9
6
5399-4
5434-1
6468-4
5402
5437
5471
9
5
9
5406-3
5441
5475-3
5409
5444
5478
8
4
7
5413-3
5447-8
5482-1
5416-7
5451-3
5485-6
3 5
3 5
3 4
208
209 !
210 '
4 5488-9
5522-8
5556 4
5492-3
5526 2
5559-8
6495
5529
6563
7
6
1
5499
5532
6566
1
9
4
5502-5
5536-3
5569 8
5505
5539
6573
9
7
1
5509 3
5543
6576 5
5512
5546
5579
7
4
8
5516-1
5549-7
5583-1
6519-4
5553-1
6586-4
3 4
3 4
3-3
211
212
213
4 5589-7
6622-8
5655-5
5593
6626-1
6658-8
5596
5029
5662
4
3
5599
5632
5665
7
6
3
5603-0
5635-9
5668-6
5606
5639
5671
3
2
8
5609-6
5642-5
6675 - 1
5612
5645
5678
9
7
3
5616-2
5649-0
5681-5
5619-5
5652-3
5684-8
3 3
3-3
3-2
214 '
215 !
216
4 5688
6/20-2
6752-2
5691 2
5723-4
5755-4
5694
5726
5758
5
6
6
5697
5729
5761
7
9
8
5700-9
5733-1
6764 9
5704
5736
5768
2
3
1
5707-4
5739-5
6771-3
5710
5742
5774
6
6
4
5713-8
5745-8
5777-6
5717-0
6749-0
6780 8
3 2
3 2
3 2
217 '
218
219
4 5783 9
5815-4
5846 6
5787-1
5818-5
5849 7
6790
5821
6852
2
6
8
5793
5824
5855
4
8
9
5796-6
5827-9
5859
5799
5831
5862
7
1
5802-9
6834 1
5865-2
5806
5837
5868
3
3
5809-1
5840-4
5871-4
5812-2
6843 5
5874-4
3 1
3 1
3 1
220
221
222
4 5877-5
5908 3
5938-7
5880-6
5911 3
5941-8
«883
5914
6944
7
4
8
5886
5917
5947
8
4
8
6889-9
5920-5
5950-9
5893
6923
5963
6
9
5896-0
5926-6
5956-9
5899
5929
5959
1
6
9
5902-1
5932-7
6963-0
5905 2
5935-7
5966-0
3 1
3
3
223
224 :
225
4 5969-0
5999
6028 7
5972-0
6002
6031 7
5975
6004
6034
9
6
6978
6007
6037
9
6
5981
6010 9
6040-5
5984
6013
6043
9
5
5987-0
6016 9
6046 5
5990
6019
6049
8
4
5993-0
60-22 8
6052 4
5996-0
6025-8 1
6055 3 j
6084 7 '
6113-8
6142-8
30
3
3
226
227 j
228
4 0058-3
6087-6
6116-7
6061-2
6090 5
6119 6
6064
6093
6122
1
4
5
0067-1
C0'.)6 3
6125 4
0070-0
6099-3
6128 3
6072
6102
6131
9
2
-2
6075-9
6105 1
6134 1
6078
6108
6137
8
6081-7
6110 9
0139-9
2 9
2 9
29
2^-0 ^
4 6145 -7
6174-6
6148-6
6177-5
6151 5
6180-4
6154-4
6183-3
6157 3
6186-2
6160
6189
1
4
6163 1
6191-9
6166
6194
8
6168 8
6197-7
6171 7
6200-6
2-9
2 9
62
XX. — EXTERIOR BALLISTICS.
Table IV.*
Inclination and Velocity Table, Cd — d^, — S^„.
V.
1
2
3
4
5
6
7
8
9
f.8.
40
41
42
d(
4
9
?g8.
6757
0056
Cl(
5
9
3g8.
4838
1240
4207
d
5
9
9640
5688
8327
d(
1
6
10
4407
0101
2410
d(
1
6
10
3ff8.
9137
4482
6467
d
2
6
11
3^8.
3830
8828
0496
d
2
7
11
3S8.
8488
3141
4494
d
3
7
11
3110
7421
8462
d
8
12
3^8.
7689
1660
2397
degs.
4-2240
8-5874
12-6306
43
13
16
20
0187
7450
2125
13
17
20
4039
1030
5460
13
17
20
7862
4585
8772
14
17
21
1652
8110
2054
14
18
21
5419
1614
5320
14
18
21
9159
5094
8565
15
18
22
2872
8549
1788
15
19
22
6557
1980
4989
16
19
22
0211
5383
8169
16-3843
19.8766
23 1327
46
47
48
23
26
29
4463
4691
3006
23
26
29
7578
7607
5739
24
27
29
0671
0503
8455
24
27
30
3736
3376
1151
24
27
30
6788
6234
3833
24
27
30
9821
9075
6498
25
28
30
2C34
1897
9147
25
28
31
5927
4702
1779
25
28
31
8801
7486
4393
26 1756
29-0254
31-6993
49
60
ei
31
34
36
9576
4557
8073
32
34
37
2143
6973
0349
32
34
37
4695
9375
2613
32
35
37
7227
1761
4862
32
35
37
9747
4134
7099
33
35
37
2253
6493
9323
33
35
38
4743
8837
1534
33
36
38
7219
1167
3731
33
36
38
9679
3480
5914
34 2125
36-5783
38-8086
52
53
54
39
41
43
0246
1175
0967
39
41
43
2394
3204
2887
39
41
43
4529
5221
4795
39
41
43
6651
7225
6690
39
41
43
8762
9221
8578
40
42
44
0860
1205
0456
40
42
44
2947
3179
2324
40
42
44
5022
5142
4182
40
42
44
7083
7095
6031
40-9135
42-9037
44-7870
55
56
57
44
46
48
9698
7437
4270
45
46
48
1510
9160
5906
45
47
48
3325
0874
7534
45
47
48
5122
2581
9153
45
47
49
6910
4277
0764
45
47
49
8689
5965
2368
46
47
49
0457
7644
3963
46
47
49
2217
9314
5551
46
48
49
3964
0973
7130
46-5705
48-2625
49-8701
58
59
60
50
51
53
0265
5492
0003
50
51
53
1822
6975
1417
50
51
53
3370
8451
2825
50
51
53
4909
9917
4224
50
52
53
6442
1378
5618
50
52
53
7968
2832
7005
50
52
53
9487
4280
8386
51
52
53
0999
5721
9761
51
52
54
2505
7155
1130
51-4002
52-8583
54-2492
61
62
63
54
55
56
3847
7054
9663
54
55
57
5196
8342
0891
54
55
57
6539
9623
2114
54
56
57
7875
0899
3330
54
56
57
9205
2169
4542
55
56
57
0529
3433
5749
55
56
57
1846
4690
6950
55
56
57
3158
5942
8146
55
56
57
4462
7188
9338
55-5761
56-8428
58-0523
64
65
66
58
59
60
1703
3209
4207
58
59
60
2878
4332
5280
58
59
60
4046
5449
6348
58
59
60
5209
6562
7411
58
59
60
6367
7669
8470
58
59
60
7521
8772
9523
58
59
61
8669
9869
0572
58
60
61
9832
0961
1616
59
60
61
0949
2047
2654
59-2081
60 3130
61-3688
67
68
69
61
62
63
4719
4779
4414
61
62
63
5744
5761
5356
61
62
63
6766
6739
6294
61
62
63
7783
7711
7227
61
62
63
8796
8680
8157
61
62
63
9804
9646
9084
62
63
64
0808
0607
0006
62
63
64
1807
1565
0924
62
63
64
2802
2519
1838
62 3793
63-3468
64 2749
70
71
72
64
65
66
3656
2522
1015
64
65
66
4559
3388
1845
64
65
66
5459
4250
2671
64
65
66
6356
5107
3494
64
65
66
7249
5962
4313
64
65
66
8137
6813
5128
64
65
66
9022
7660
5940
64
65
66
9903
8504
6749
65
65
66
0779
9345
7553
65-1652
66-0182
66-8355
73
74
75
66
67
68
9153
6955
4436
66
67
68
9949
7717
5168
67
67
68
0740
8476
5896
67
67
68
1529
9231
6620
67
67
68
2314
9983
7342
67
68
68
3096
0733
8062
67
68
68
3875
1479
8778
67
68
68
4649
2223
9492
67
68
69
5422
2964
0204
67-6190
68-3702
69 0912
76
77
78
69
69
70
1617
8497
5082
69
69
70
2318
9169
5725
69
69
70
3017
9838
6365
69
70
70
3712
0503
7004
69
70
70
4404
1166
7639
69
70
70
5094
1826
8271
69
70
70
5780
2483
8901
69
70
70
6464
3137
9527
69
70
71
7145
3787
0149
69-7823
70-4436
71-0770
79
80
81
71
71
72
1388
7432
3225
71
71
72
2004
8023
3791
71
71
72
2617
8611
4354
71
71
72
3228
9196
4915
71
71
72
3837
9779
5473
71
72
72
4442
0359
6030
71
72
72
5045
0937
6584
71
72
72
5646
1513
7135
71
72
72
6244
2086
7685
71-6839
72 2656
72-8232
82
83
84
72
73
73
8776
4079
9143
72
73
73
9317
4596
9636
72
73
74
9856
5111
0127
73
73
74
0393
5622
0615
73
73
74
0927
6132
1101
73
73
74
1458
6639
1585
73
73
74
1988
7145
2067
73
73
74
2514
7648
2546
73
73
74
3038
8149
3023
73-3560
73-8647
74-3498
85
86
87
74
74
75
3971
8573
2966
74
74
75
4441
9022
3395
74
74
75
4910
9468
3821
74
74
75
5376
9912
4246
74
75
75
5839
0355
4668
74
75
75
6301
0795
5089
74
75
75
6760
1233
5507
74
75
75
7217
1669
5924
74
75
75
7670
2104
6339
74-8123
75-2536
75-6752
By W. D. Kiven, Esq., M. A., F. S. S.
XX. EXTERIOR BALLISTICS.
Table lY .—Continued.
Inclination and Velocity Table, Cd = 8^ — S^„
V.
1
!3
3
4
5
6
7
8
9
f.8.
88
89 1
90
degs.
75 7163
76 1171
76-5005
degs.
75-7572
76-1562
76-5379
degs.
75-7980
76-1952
76-5751
degs.
75 8385
76-2339
76 6121
degs.
75-8788
76-2725
76-6490
degs.
75-9190
i 76-3109
76-6857
degs.
75 9590
76-3492
76-7223
degs.
75-9988
76-3873
76-7588
d
76
76
76
4252
7951
degs.
76-0778
76-4629
76 8312
91
92
93
76-8671
77-2179
77-5540
76-9029
77-2522
77-5868
76-9385
77-2863
77-6195
76-9739
77-3203
77-6520
77-0092
77-3541
77-6844
77-0444
77-3878
77-7167
77 0794
77 4213
77-7488
77-1142
77-4547
77-7807
77
77
77
1489
4879
81-25
77-1835
77-5210
77 8442
94
95
96
77-8757
78 1841
78-4798
77 9071
78-2142
78 5087
77-9384
78-2442
78-5375
77-9695
78-2741
78-5622
78-0005
78 3039
78-5947
78-0314
78-3335
78-6231
78 0622
78-3630
78-6514
78-0929
78-3924
78-6796
78
78
78
1234
4216
7076
78 1538
78 4508
78 7356
97
98
99
78-7634
79-0354
79-2968
78-7911
79 0621
79-3224
78-8188
79-0886
79-3478
78 8463
79 1150
79-3731
78-8736
79 1413
79-3983
78-9009
79 1675
79-4234
78-9280
79 1936
79-4484
78-9551
79-2195
79-4734
78
79
79
9819
2454
4982
79-0087
79-2712
79 5230
100
101 1
102
79-5476
79-7889
80-0203
79-5722
79-8124
80 0430
79-5966
79-8359
80-0655
79-6210
79-8593
80-0879
79-6453
79-8826
80 1102
79 6695
79-9058
80 1324
79-6935
79 9289
80-1544
79-7175
79-9519
80-1763
79
79
80
7414
9748
1981
79 7652
79-9976
80-2197
103
104
105
80-2412
80-4466
80-6321
80-2625
80-4661
80-6495
80-2837
80-4854
80-6667
80-3408
80-5045
80-6835
80-3256
80 5234
80 7003
80-3462
80 5420
80 7169
80 3667
80 5605
80 7333
80-3869
80-5787
80-7495
80
80
80
4071
5967
7654
80-4270
80 6145
80 7813
106
107 '
108 1
80 7970
80-9463
81-0841
80-8126
80-9606
81-0973
80-8280
80-9747
81 1105
80-8432
80-9886
81 1236
80-8583
81 0026
81 1366
80-8733
I 81 0164
81 1495
80-8882
81-0301
81 1624
80 9029
81 0437
81 1751
80
81
81
9175
0573
1877
80-?319
81 0707
81 2003
109
110
lllj
81-2129
81-3342
81-4495
81-2253
81-3460
81-4607
81-2377
81-3578
81-4719
81 2501
81 3695
81 4829
81-2623
81-3811
81 4939
81-2745
81-3927
81 5049
81-2866
81-4042
81-5159
81-2986
81-4156
81-5268
81
81
81
3105
4269
5377
81-3224
81 4382
81 5486
112
113
114 !
81-5593
81-6647
81 7662
81-5700
81-6750
81-7761
81-5807
81-6853
81-7861
81-5913
81-6955
81-7960
81-6019
81-7057
81-8058
81-6124
81 7159
81-8156
81-6230
81-7260
81-8254
81-6334
81-7361
81-8351
81
81
81
6439
7462
8448
81-6543
81-7662
81 •8545
115
116
117
81-8641
81-9588
82-0503
81-8737
81-9681
82-0592
81-8833
81-9774
82-0682
81-8929
81-9866
82 0771
81-9024
81-9958
82-0860
81-9119
82-0049
82 0948
81-9213
82 0141
82 1036
81-9307
82-0232
82 1124
81
82
82
9401
0322
1212
81-9496
82 0413
82-1299
118
119
120
82 1386
82-2241
82-3066
82-1473
82-2325
82-3147
82 1559
82-2408
82-3228
82 1645
82-2492
82 3309
82 1731
82-2575
82-3389
82-1817
82-2657
82-3469
82-1902
82-2Y40
82-3549
82-1988
82-2822
82-3629
82
82
82
2073
2903
3708
82-2157
82-2985
82-3787
121
122
123
82-3865
82-4639
82 5386
82-3944
82-4715
82-5459
82-4022
82-4790
82 5533
82-4100
82-4865
82-5606
82-4178
82-4940
82-5679
82-4255
82 5015
82-5751
82-4333
82-5090
82-5824
82-4410
82-5164
82-5896
82
82
82
4486
5238
5968
82-4563
82-5312
82 6040
124
125
126
82-6112
82-6814
82-7494
82-6183
82-6883
82-7561
82-6254
82-6951
82-7627
82 6324
82-7019
82 7694
82-6395
82-7088
82 7760
82-6465
82-7156
82-7826
82-6535
82-7224
82-7892
82-6605
82-7291
82-7957
82
82
82
6675
7359
8023
82-6744
82-7427
82-8088
127
128
129
82-8153
82-8794
82-9415
82-8218
82-8857
82-9477
82-8283
82-8920
82-9538
82-8348
82-8983
82-9599
82-8412
82-9045
82-9660
82-8477
82-9107
82-9720
82-8541
82-9169
82-9780
82-8604
82-9231
82-9840
82
82
82
8668
9292
9900
82-8731
82-9354
82-9900
130
131
132
83-0019
83 0606
83 1176
83-0079
83-0664
83 1232
83-0138
83-0721
83-1288
83 0197
83-0779
83-1344
83-0256
83-0836
83-1400
83 0315
83-0893
83 1455
83-0373
83 0950
83 1511
83-0432
83-1007
83 1566
83
83
83
0490
10^3
1621
83 0548
83-1119
83-1676
133
184
136
83-1730
83-2271
83-2797
83-1785
83-2324
83-2849
83 1840
83-2377
83-2900
83-1894
83-2430
83-2951
83 1949
83-2483
83-3003
83-2003
83-2536
83-3054
83-2057
83-2588
83-3105
83 2110
83-2641
83-3156
83
83
83
2164
2693
3207
83 2217
83 2745
83-3257
64
XX. — EXTERIOR BALLISTICS.
Table lY .—Continued.
Inclination and Velocity Table, Cd = d^,
..
1
2
3
4
5
6
7
8
"
f.s.
136
137
138
degs.
83-3308
83-3808
83-4295
d(
83
83
83
5gS.
3359
3857
4343
degs.
83-3409
83-3906
83-4391
degs.
83-3459
83-3955
83-4438
d(
83
83
83
3509
4004
4486
d(
83
83
83
3560
4053
4533
d<
83
83
83
3g8.
3609
4101
4581
d(
83
83
83
5g8.
3659
4150
4628
d(
83
83
83
3g8.
3709
4198
4676
degs.
83-3759
83-4247
83-4723
139
140 '
141
83
83
83
4770
5233
5687
83
83
83
4817
5279
5732
83-4863
83-5325
83-5777
83-4910
83-5371
83-5821
83
83
83
4956
5417
5866
83
83
83
5003
5402
5910
83
83
83
5049
5507
5954
83
83
83
5095
5553
5999
83
83
83
5141
5598
6043
83-5187
83-5642
83-6087
142
143
144
83
83
83
6130
6565
6988
83
83
83
6174
6607
7030
83-6218
83 - 0650
83-7072
83-6261
83-6693
83-7114
83
83
83
6305
6735
7156
83
83
83
6348
6778
7197
83
83
83
6392
6820
7239
83
83
83
6435
6862
7280
83
83
83
6478
6904
7321
83-6522
83-6946
83-7362
145 \
146 i
147
83
83
83
7403
7810
8209
83
83
83
7444
7850
8249
83-7485
8.3-7891
83-8-288
83-7526
83-7930
83 8327
83
83
7567
7970
8366
83
83
83
7608
8010
8406
83
83
83
7649
8050
8445
83
83
83
7689
8090
8484
83
83
83
7730
8130
8522
83-7770
83 '8170
83-8561
148
149
150
83
83
83
8600
8983
9359
83
83
83
8639
9021
9396
83-8677
83-9059
83-9433
83-8715
83 9096
83-9470
83
83
83
8754
9134
9507
83
83
83
8792
9172
9544
83
83
83
8830
9209
9581
83
83
83
8869
9247
9617
83
83
83
8907
9285
9654
83-8945
83-9322
83-9691
151 '
152
153
83
84
84
9727
0090
0446
83
84
84
9764
0126
0481
83-9800
84-0161
84-0516
83-9837
84-0197
84-0551
83
84
84
9873
0233
0587
83
84
84
9909
0269
0622
83
84
84
9946
0304
0657
83
84
84
9982
0340
0692
84
84
84
0018
0375
0727
84-0054
84-0410
84-0762
15.
155
156
84
84
84
0796
1140
1479
84
84
84
0831
1174
1513
84-0866
84 1208
84-1546
84-0900
84-1242
84-1579
84
84
84
0935
1276
1613
84
84
84
0969
1310
1646
84
84
84
1004
1344
1679
84
84
84
1038
1378
1713
84
84
84
1072
1412
1746
84-1106
84 1445
84-1779
157
158
159
84
84
84
1812
2139
2461
84
84
84
1845
2172
2493
84-1878
84-2204
84-2525
84-1911
84-2237
84-2557
84
84
84
1943
2269
2588
84
84
84
1976
2301
2620
84
84
84
2009
2333
2652
84
84
84
2041
2366
2683
84
84
84
2074
2398
2715
84-2107
84-2430
84-2746
160 '
161
162
84
84
84
2778
3088
3394
84
84
84
2809
3119
3424
84-2840
84-3150
84-3454
84-2871
84-3180
84-3484
84
84
84
2902
3210
3514
84
84
,84
2933
3242
3544
84
84
84
2965
3272
3574
84
84
84
2996
3302
3604
84
81
84
3027
3333
3634
84-3058
84-3363
84-3664
163
164
165
84
84
84
3694
3990
4281
84
84
84
3724
4019
4310
84-3753
84-4018
84-4339
84-3783
84-4078
84-4367
84
84
84
3813
4107
4396
84
81
84
3843
41S6
4425
84
84
84
3872
4105
4453
84
84
84
3902
4194
4482
84
84
84
3931
4223
4510
84-3960
84-4252
84-4539
166
137
168
84
84
84
4567
4849
5127
84
84
84
4595
4877
5154
84-4624
84-4905
84-5181
84-4652
84-4933
84-5209
84
84
84
4680
4961
5236
84
84
84
4709
4988
5263
84
84
84
4737
5016
5291
84
84
84
4765
5044
5318
84
84
84
4793
5070
5345
84-4821
84-5099
84-5372
169
170
171
84
84
84
5399
5668
5933
84
84
84
5426
5695
5959
84-5453
84-5721
84-5985
84-5480
84-5748
84-6012
84
84
84
5508
5775
6038
84
84
84
5534
6801
6064
84
84
84
5561
5828
6090
84
84
84
5588
5854
6116
84
84
84
5615
5880
6142
84-5641
84-5907
84 0168
172
173
174
84
84
84
6193
6449
6701
84
84
84
6219
6475
6726
84-6245
84-6500
84-6750
84-6271
84-6525
84-6776
84
84
84
6297
6550
6800
84
84
84
6322
6575
6825
84
84
84
6348
6001
6850
84
84
84
6373
6626
6875
84
84
84
6399
6651
6899
84-6424
84-6676
84-6924
175
176
177
84
84
84
6948
7192
7432
84
84
84
6973
7216
7455
84-6997
84-7240
84-7479
84-7022
84-7264
84-7503
84
84
84
7046
7288
7526
84
84
84
7071
7312
7550
84
84
84
7095
7336
7574
84
84
84
7119
7360
7597
84
84
84
7144
7384
7621
84-7168
84-7408
84-7645
178
179
180
81
84
84
7608
7P02
8131
84
81
84
7692
•7925
8154
81 -771 5
84-7918
84-8177
84-7739
81-7972
8i-8199
84
81
84
7762.
7904
8222
•84
81
81
7785
roi7
8214
84
84
84
7809
80 :o
82u7
84
84
84
7832
803
8289
84
84
84
7855
80SG
8312
84-7878
81-8109
84-8334
181
182
183
84
84
84
83R7
8579
8798
81
84
84
8379
8601
8819
84-8-101
84-8623
84-8841
81 ■ 8424
84-8645
84-8863
84
84
84
8446
8667
8884
84
i ^*
8168
8689
8906
84
84
84
81 PO
8711
8927
84
84
84
8513
8732
8949
84
84
84
8535
8754
8970
84-8557
84-8776
84-8992
XX. — EXTERIOR BALLIStlCS.
Table IV.— Continued.
Inclination and Velocity Table, Cd = S^, — S^„.
V.
1
2
3
4
5
6
7
8
f.s.
184
185
186
d
84
84
84
9013
9226
9435
d
84
84
84
egs.
9035
9247
9456
d
84
84
84
9056
9268
9476
d
84
84
84
egs.
9077
•9289
9497
d
84
84
84
egs.
•9099
•9310
9518
d
84
34
84
9120
9331
•9538
d
84
84
84
egs.
9141
9351
•9559
degs.
84-9162
84 9372
84-9580
d
84
84
84
egs.
■9184
■9393
-9600
degs.
84-9205
84 9414
84-9621
1?7
188
189
84
84
85
9C41
•9845
0045
84
84
86
9C62
9865
0065
84
84
85
9682
9885
0085
84
84
85
9702
9905
0105
84
84
85
9723
9925
0125
84
84
85
•9743
•9946
•0145
84
84
85
9763
•9966
0165
84 • 9784
84-9986
85 0185
84
85
85
9804
0006
0204
84-9820
86-0026
85-0224
190
191
192
85
85
85
0244
0438
0630
85
85
85
0263
0458
0650
85
85
85
0283
0477
0669
85
85
85
0303
0496
0687
85
85
85
0322
0515
0706
85
85
85
0342
0535
0725
85
85
85
•0361
0554
0744
85 0380
86 0573
85 0763
85
85
85
0400
0592
0782
8.'5 0419
85-0611
85-0801
193
194
195
85
85
85
0820
1006
1190
85
85
85
0838
1025
1208
85
85
85
0857
1043
1227
86
86
85
0876
10C2
1245
85
85
85
0895
1080
1263
85
85
85
0913
1099
1281
85
85
85
•0932
1117
1299
85 0951
85 1136
85 1317
85
85
85
0969
1154
1335
85-0988
86 1172
85 -136a
196
197
198
85
85
85
1371
1549
1724
85
86
85
1389
1567
1741
85
85
85
1407
1584
1759
85
85
85
1425
1602
1776
85
85
85
1443
1619
1793
85
85
85
1460
1637
1810
85
85
85
1478
1654
1827
85 1496
85-1672
85 1844
85
85
85
1514
1689
1862
86-1531
85 1707
86-1879
199
200
201
85
85
85
1896
2065
2231
85
85
85
1913
2081
2247
85
85
85
1930 '
2098
2264
86
85
85
1947
2115
2280
85
85
85
1964
2131
2290
84
85
85
1981
2148
2313
85
85
85
1998
2165
2329
85 2014
85-2181
85-2346
85
85
85
2031
2198
2362
86-2043
85-2214
85-2378
202
203
204
85
85
85
2394
2556*
2714
85
85
85
2411
2572
2729
85
85
85
2427
2588
2745
85
85
86
2443
2604
2760
86
85
85
2459
2620
2776
85
85
85
2476
2635
2791
85
85
86
2492
2651
2807
85 2507
85-2667
85-2822
85
85
86
2524
2682
2838
85-2540
85-2698
85-2863
205
206
207
85
85
85
2868
3020
3170
85
86
85
2884
3035
3184
86
85
85
2899
3061
3199
86
85
85
2915
3066
3214
85
85
85
293C
3081
3229
86
85
2945
3095
3244
85
85
86
2960
3110
3258
85 2975
85-3125
85-3273
85
85
85
2990
3140
3287
85-3005
85 3165
85-330a
208
209
210
85
85
85
3316
3460
3601
85
85
85
3331
3474
3615
85
85
85
3345
3488
3629
85
85
86
3360
3503
3643
85
85
85
3373
3517
3657
85
85
85
3388
3531
3671
86
85
85
3403
3546
3685
86 3417
85-3559
85-3698
85
85
85
3431
3573
3712
85-3446
85-3581
85 3726
211
212
213
85
85
85
3740
3876
4010
85
85
88
3754
3890
4023
85
85
85
3767
3903
4036
85
85
85
3781
3917
•4049
85
85
85
3795
3930
4063
85
85
85
3808
3943
4076
85
85
85
3822
3957
4089
85 3836
85 3970
85-4102
85
85
86
3849
3983
4115
85-3863
85-3996
85 4128
21^
215
216
85
85
85
4141
4271
4398
85
85
85
4154
4284
4411
85
86
85
4167
4297
4423
85
86
85
4180
4309
4436
85
85
85
4193
4322
4448
85
85
85
4206
4335
4461
85
85
86
4219
4348
4473
85-4232
85-4360
85-4485
86
85
85
4245
4373
4498
85-4258
85-4385
86-4510
217
218
219
85
85
85
4523
4645
4766
85
85
85
4535
4658
4778
85
85
85
4547
4670
4790
85
85
85
4560
4682
4802
85
85
86
4572
4694
4814
85
85
85
4584
4706
4825
85
85
85
4597
4718
4837
85-4609
85-4730
85-4849
85
85
86
4621
4742
4861
86-4633
86-4754
86-4873
220
221
222
85
85
85
4885
5001
5116
85
85
85
4896
5013
5128
86
85
85
4908
5024
5139
85
86
86
4920
6036
6150
85
85
85
4932
5047
5162
86
85
85
4943
5059
5173
85
85
85
4965
6070
6184
85-4967
85-5082
85 5195
86
85
86
4978
5093
5207
85-4990
85-6105
85-5218
223
224
225
85
85
85
5229
5340
5449
85
85
85
5240
5351
5460
85
85
85
5251
5362
5470
85
85
85
5262
5373
6481
85
85
85
5273
5384
5492
85
85
86
5285
5394
5502
85
85
85
5296
5405
5513
85-5307
85-5416
86-5624
86
85
85
5318
5427
5534
85-5329
86-5438
86-6545
226
227
228
85
85
85
5556
5661
5765
85
85
85
5566
5672
6775
85
85
85
5577
5682
5785
85
85
85
5688
6693
5796
86
85
85
6598
5703
5806
86
85
85
5609
5713
5816
85
86
86
5619
5724
5826
85-5630
85-5734
85-5836
85
85
85
5640
5744
5846
85-5651
85-5755
85-5856
229
230
85
85
5866
5966
85
85
5876
5976
85
85
5886
5986
85
85
5896
5996
85
85
5906
6006
85
85
5916
6015
85
85
6926
6025
85 5936
85-6035
85
85-
5946
6045
85-5956
85-6055
XXI. — VARIETIES OF CANNON.
CHAPTER XXI.
VARIETIES OF CANNON.
CLASSIFICATION.
The numerous ways in which cannon may be classified
have been simpHfied by the almost universal adoption of
those which are breech-loading rifies^ built up of steel.
For convenience of treatment we may consider them ac-
cording to t\\Q\v proportions, construction and service,
1. Proportions.
The facility with which breech-loading cannon of all
lengths may be loaded has practically abolished the distinc-
tion between mortars and howitzers, although both terms are
still used for pieces which do not differ materially in their
proportions.
It has become customary to distinguish guns (Chapter I)
from howitzers by calling the first named rifles, although all
new howitzers are also rifled.
2. Construction.
As to construction, cannon are divided into muzzle-loaders
and breech-loaders; some of the former class being still re-
tained in service pending the preparation of those of the better
type and also for subordinate purposes.
Breech-loaders may be divided into those having but one
barrel, or single fire pieces, which are loaded by hand, and
into machine guns, in which the loading is automatically per-
formed by machinery. The former may be either the com-
paratively slow fire cannon, in which the cartridge and
projectile are loaded separately, or the rapid fire in which
XXI. VARIETIES OF CANNON.
the ammunition makes but one package, as in small arms,
and the recoil of which does not derange the aim.
Machine guns generally consist of a number of barrels so
disposed, that while one is firing, the remainder may be
loaded and prepared for loading. Like the rapid fire cannon
these require metallic ammunition, and unlike them their size
is imited by the weight of the required number of cartridges
which can be conveniently kept in motion by the machinery ;
the latter is generally operated by hand.
3. Service.
According to their employment, cannon are divided into
those for the mountain, field, siege and sea coast services.
The principal distinction here refers to the difficulties of
transportation, for the rule is general that the most power-
ful cannon that can be efficiently transported should always
be employed.
For field artillery especially, the principle of independence
of function requires a very exact adaptation of the weight of
the arm to the service required of it. Thus, we have, 1st,
Horse Artillery, which, the cannoneers being mounted on
horses, may accompany the Cavalry ; 2nd, Light Field Ar-
tillery, which manoeuvres with Infantry ; and 3rd, Heaiy Field
Artillery, which forms batteries of position at important tacti-
cal points, and is intended to engage at long ranges.
This affords the following table :
CLASSIFICATION OF ARTILLERY ACCORDING TO
1 P.-r,^^rt;r.nc S Guiis, for direct fire.
1. rioporuons ^ Howitzers, or Mortars for curved fire.
r Muz de loading ^Smoothbore.
I (obselete, retained) \ Rifled.
2. Construction \ ' i c- „, <-_ ( slow.
' * ( ■ ( slow,
j Breech loading rifles ) ^'"^le fire | ^.^p- j^
( Machine guns,
XXI. — VARIETIES OF CANNON.
3. Service.
Mountain.
i Horse Artillery, very light.
Field < Light Field Artillery, medium.
f Heavy Field Artillery.
Siege.
Sea Coast.
SYSTEM OF ARTILLERY.
This term refers to the character and arrangement of the
materiel* as adopted by a nation at any particular epoch.
The principal requisites of a system of artillery are sim-
plicity^ mobility and power. To these the enormous arma-
ments of the present day may add economy.
The improvements of the last four hundred years have had
these qualities in view, the compromises between simplicity
and mechanical efficiency, noted Chapter XVI, causing
sometimes one, and sometimes another of these qualities to
pieponderate.
As in other nations the system of artillery in the United
States service is still in an experimental state.
For lack of funds, withheld largely because of uncertainty
regarding the direction of improvement, many obsolete
weapons have been retained by us either unchanged, or
converted so as to increase their power at a moderate expense.
The following description is therefore partly historical, and
contains incidental reference to methods adopted in other
countries whose political situation has made their immediate
armament urgent. It is confined to slow fire guns, since
other types of breech-loaders depend for their efficiency
almost wholly upon the control of their recoil and upon the
use of metaUic ammunition; subjects not yet discussed. See
Chapter XXIX.
* See Webster,
XXr. — VARIETIES OF CANNON.
CONSTRUCTION.
I. MUZZLE LOADING CANNON.
United States.
The field guns used during the Civil War were of two
kinds.
1. The 3 ijich wrought iron (10 pdr^ rifle.
This was made by wrapping boiler plate around a wrought
iron bar to form a rough cyUnder, which was welded
together under the rolls and finished in the usual manner.
It made a very strong, light gun well adapted to the
Horse Artillery.
2. The 12 pdr. Napoleon Gun^ S7nooth bore.
This was of bronze, cast solid. Its value depended upon
the topography of the seat of war.
The broken surface of the Appalachian system and the
heavy woods with which much of the country was covered
restricted the fighting to ranges which, compared to those
obtainable on the broad plains of Europe, are very moderate.
For such ranges its heavy shell and well filled shrapnel were
more efiective than those of the rifle, and the initial velocity
was so great that for ranges of about 1000 yards the trajectory
of the smooth bore was flatter than that of the rifle.
The siege gims, in which mobility was less important, were
of cast iron. Owing to the length of the bore and its rela-
tively small diameter these guns were cast solid. The pro-
jectile weighed about 30 pounds.
One of these pieces, the Parrott, was strengthened by a
wrought iron cylinder shrunk over the breech and reinforce.
In order to prepare so massive a forging a hot iron bar was
coiled helically around a mandrel, brought to a welding heat
and forged by axial blows of the hammer. To prevent
XXr. — VARIETIES OF CANNON.
distortion during welding, the coil was held in a hollow cyl-
inder. Several coils would be similarly welded end to end.
The direction of the fibers gave great tangential tenacity, but
for reasons given in Chapters XV, page 60, and XIX, page
12, the construction was faulty.
Sea coast guns were generally of cast iron, cast hollow on
the Rodman principle. To some the Parrott construction
was applied.
Since 1875 many Rodman guns have been converted on
the Palliser (English) plan by reaming out the bores to receive
a thick, wrought-iron tube, which was then rifled. Chapter
XIX.
These tubes, first made by coiling as above described, were
ultimately replaced by those of solid steel, the intrinsic
strength of which was almost sufficient.
The wrought-iron tube was at fiist inserted from the muzzle ;
but, as it was liable to be carried out with the projectile, a
stronger but much more costly breech insertion was employed.
With steel, which presented no false welds for the action
of the powder gases, the muzzle insertion was resumed.
In this way many 10 inch smooth-bore Rodman guns were
altered to 8 inch rifles. The 15 inch Rodman guns are re-
tained unchanged for subordinate purposes.
Foreign Services.
Abroad a similar course was followed. In France^ the old
cast-iron guns were hooped with puddled steel, originally to
retain the fragments on explosion. The bores were lined
with a short steel tube. This method is now followed for
subordinate pieces of large caliber.
Engla7id tried the Palliser plan of conversion for her old
guns. For new guns wrought iron was at first exclusively
employed ; then wrought iron coils on a steel tube were used,
XXI. — VARIETIES OF CANNON.
and finally with breech loaders steel throughout. The fear
of the brittleness of steel, the consequent preference for the
weaker though more ductile wrought iron, and the indiffer-
ence to the molecular treatment of steel as practiced by their
more exact neighbors, the French, have cost the English
Government much loss in time and money.
To Krupp, in Germany, belongs the credit of first using
steel in large masses. The weight of his ingots has increased
since 1851 from two tons to seventy.
The construction of his cannon now requires relatively
large units of construction. The tendency elsewhere is to
reduce the weight of the maximum unit so as to avoid the
large outlay for plant required only for its manufacture and
handling. For it must be remembered that although cannon
comprise the heaviest masses now made, yet their commercial
importance is relatively small. Chapter XIV, page 2.
II. BREECH LOADING CANNON.
These may be classified according to the means by which
the breech is closed ; but, as this depends largely upon the
form of gas check employed, this will be first discussed.
1. Gas Checks.
Many early efforts were made to prevent the escape of gas
by some rigid fastening after the manner of a plug ; but, owing
to the erosion through the slightest crevice caused by dust,
rust or fouling, the efficiency of these devices was short-lived.
The self-sealing gas check alone made breech loading prac-
ticable. Gas checks may be classified according as they are
attached to or detached from the breech block.
Detached Gas Checks.
The ordinary metallic cartridge case is the best example of
this class. The flexibility of its walls and its renewal at every
fire peculiarly adapt it for this purpose.
XXI, — VARIETIES OF CANNON^
But, since it would be impracticable to use cartridges of
the size required for heavy cannon, the cartridge case may be
replaced by a short permanent ring as shown in figure 1.
This represents one form of an American invention, the
Broadwell ring, r, with its obturator plate, /.
The gaseous pressure expands the thin edge laterally
against the seat in the tube and also presses the ring bodily
backward against the plate. The annular grooves, g, in the
base of the ring serve as air packing ; they also increase the
intensity of the pressure on a vital surface, and, with the hol-
low, h, collect any fouUng, which might otherwise occur on
this surface.
The surface^ s, is spherical so as to adjust itself easily to he
spherical seat of the ring around the mouth of the chamber,
past which the obturator plate is caused to slide by the motion
of the breech block to which it is attached.
This form of gas check is difficult to maintain, as it is diffi-
cult to prevent entirely the escape of gas between the ring
and the plate.
Attached Gas Checks,
These necessarily require some motion of the block in the
direction of the axis of the piece and across the joint to be
sealed.
Figure 2 represents the Freyre gas check of Spanish origin.
It consists of a steel ring, r, of triangular cross-section sur-
rounding a conical wedge, w. This last is formed with a
spindle, 5, passing axially through the breech block, B, The
stem is surrounded by a spiral spring against which it acts by
a shoulder. The thickness of the wedge is slightly less than
that of the ring.
The gases press the wedge backward and thus expand the
ring ; when they cease to act the spring moves the wedge
forward and thus prevents the ring from sticking in its seat.
Figure 3 represents the De Bange (French) gas check, de-
XXI. — VARIETIES OF CANNON
rived from that used in the Chassepot b 1, rifle, a small arm
firing a non-metallic cartridge The steel ring of figure 2 is
replaced by a plastic ring, r, composed of a mixture of asbes-
tos and tallow enclosed in canvass and having the joints
through which the composition might extrude protected by-
metallic rings. When the mushroom head, h, is compressed
axially the ring, r, expands laterally, giving a pressure per
unit of area against the surface of its seat nearly equal to ^^-i- ;
in which R is the common external radius of the head and
ring, and / is the length of its bearing.
A nut on the rear end of the spindle regulates the initial
compression required for efficiency. A spring beneath the
nut relieves it from shock as the head is thrown forward after
firing by the elasticity of the tallow.
^ Comparison.
The Broadwell ring has to seal four surfaces not protected
from dirt instead of but two, and the joint, most difficult to
seal, is that which is most exposed to dirt.
Of the attached gas checks, the Freyre, being inorganic, is
less subject to extreme variations of temperature ; it also takes
up less room in the thickest part of the gun. It is open to
objection that a sHght nick on the edge of the ring might
render the entire apparatus worthless.
To the last consideration is due the almost universal
employment of the De Bange gas check, since this has been
found almost indestructible by the accidents of service and to
resume its shape when deformed in firing.
2. Fermeture.
The fermeture (French, fermer to close) is the device by
which the breech is opened and closed. Its principal requi-
sites are safety and convenience. The form of fermeture
depends largely upon the kind of gas check employed.
XXI. — VARIETIES OF CANNON.
Two principal varieties exist, the Krupp and the French
systems.
1. The Krupp or wedge system, figure 4.
Description.
The breech block, B^ moves transversely through a hori-
zontal slot in rear of the chamber. The front face of the
block is flat, and the rear surface a convex semi-cylinder whose
axis is slightly inclined to the plane of the face. This avoids
the sharp reentrant angles noted. Chapter XV, page 21. It
has been found expedient also to round the angles in front
of the slot.
The upper and lower surfaces of the slot contain guides, ^,
which are parallel to the elements of the cylindrical surface
and enter corresponding grooves in the block. The block
thus receives a component longitudinal motion in the direc-
tion of the axis of the bore which prevents friction between
the ring and the obturator plate, and also assists somewhat in
pressing the cartridge home.
A hole, h, through the block permits the gun to be loaded
when the block is withdrawn to the proper position. It is
prevented from passing this point by a stop bolt, screwed
through the body of the gun and having a blank end pro-
jecting into a groove on the upper surface of the block.
Locking.
To secure the fermeture a revolving latch^ /, is employed.
For small cannon using metallic ammunition this may be a
simple turn-button operated by an exterior handle, (9, and
entering a recess in one of the faces of the slot.
With a less perfect gas check, means must be provided for
pressing the obturator plate, /, against the ring, r, so that
for larger guns the latch consists of a screw. In order to
faciUtate the operation of the fermeture, the fillets on one
10 XXI. — VARIETIES OF CANNON.
side of the newel of the screw are removed so that a half-
turn of the screw may engage or disengage the remaining
fillets.
Translation.
For field pieces the block is withdrawn directly by hand,
but heavy pieces are provided with a long screw, S^ con-
tained in a groove in the upper part of the block, and turn-
ing in two cylindrical collars, one at each end. The rotation
of this screw in a half nut which is attached to the gun,
causes relative motion to occur between the block and the
gun.
Since for this motion speed is required, the screw is cut
with a considerable pitch. As this causes a loss of the power
required to start the block from its seat and to close it firmly,
there is supplied an auxiliary locking screw, d^ which passes
through the latch, /. By a peculiar arrangement illustrated
in a model in the Ordnance Museum, in closing the breech
this screw first turns the latch and then by its slow pitch
supplies the power required, and conversely in opening.
Both screws are operated by a T wrench, G, which is
detached.
2. The interrupted screw fermeture is commonly
known as the French system, although its origin is probably
American.
Description.
A cylindrical block fills the breech in the prolongation of
the bore and in rear of the tube.
The block is held by a screw thread which engages with
the base ring ; this in turn is screwed to the jacket by a
ratchet screw thread, Chapter XV, figure 47, and figures 2, 3
and 10, Chapter XXI.
To facilitate its operation, alternate sections, ordinarily of
XXI. — VARIETIES OF CANNON. 11
60", are removed from the adjacent surfaces of the block and
base ring, so that after sUding the block nearly into place it
may be easily locked.
Some device is required to support the block when with-
drawn. For small pieces this is supplied by the carrier ring.
This ring is provided with two lugs forming, with corre-
sponding cavities in the jacket and a vertical pin, a hinge on
which it swings to the left and rear in opening.
A stop^ a b^ Chapter XV, figure 47, screwed to the carrier
ring, enters a groove formed in one of the smooth sectors of
the block. This groove terminates in front at a short dis-
tance from the face of the block, and in rear makes a return
of 60° parallel to the screw thread.
The carrier ring also contains a shallow groove, c d, for
the head of the lever, and the latch, /, the action of which is
important. See figure 10.
The latch is pressed by a spiral spring radially inward
against the block, so that its inner extremity describes on the
smooth sector on which it rests a path parallel to the groove
in which travels the stop. We will designate the rearmost
end of this path by r, and the front end by /. At r and /
are formed cavities into which the inner end of the latch may
enter sufficiently to sink its outer end to the level of the outer
edge of the carrier ring. Each cavity is connected with the
intervening path by an inclined plane ; the cavity at / is prac-
tically a cylinder.
On the rear face of the base ring is a conical dowel, the
point of which, when the carrier ring is closed, enters a corre-
sponding cavity in the adjacent face of the carrier ring.
After passing this cavity, the point of the dowel enters a
conical hole in the front surface of the latch, and thus serves
to press it radially outward, so that when the carrier ring has
been completely closed, the inner end of the latch will have
been raised so far out of the cavity / that the block may slide
12 XXI. VARIETIES OF CANNON.
freely through the carrier ring. As it slides it forces the
outer end of the latch into its seat in the jacket.
There are three concentric pieces, the block, the carrier
ring and the jacket. The latch unites these alternately in
pairs.
Operation.
Suppose the block to be closed and locked. Raise the
lever and turn the block to the left until the stop prevents
further rotation.
In so doing, the inner end of the latch rides up the inclined
plane leading from r, and the outer end enters the jacket as
shown in the end view of figure 47, Chapter XV. This pre-
vents the obstruction to the withdrawal of the block caused
by the simultaneous swinging of the ring which would other-
wise occur.
The block can now ordinarily be freely withdrawn ; but if,
from the expansion of the gas check, it should not move
freely, an eccentric projection on the head of the lever acts
as a cam''^ and starts the block from its seat.
It is well to observe that the rotation of the block being
independent of that of the gas check, the binding of the
latter does not 'resist the initial rotation above described.
On withdrawing the block to the extent allowed by the
stop grove, the inner end of the latch drops into the cavity
f ; the carrier ring is then free to swing in continuation of
the motion of withdrawal.
After loading, these motions are reversed. In closing the
breech the latch locks the block and carrier ring together,
since any slippipg of the block through the ring would cause
the edge of the gas check to strike against the base ring.
This would be particulariy objectionable in the Freyre check.
When the carrier ring comes against the rear face of the
* See Webster.
XXI. — VARIETIES OF CANNON. IB
base ring the conical pin described lifts the pin from the hole,
/, and permits the block to slide forward until ready to en-
gage with the threads in the base ring.
After closing the breech the eccentric head of the lever
enters the groove, c d ; this prevents the unscrewing of the
block by the tangential component of the pressure on the
screw threads. This pressure is so great that it has been
found necessary to protect the bearing surface of the groove,
^^, by a plate of hardened steel.*
Variations,
For large pieces a more stable support than that offered by
the thin carrier ring is required during the withdrawal of the
block.
This is furnished by a tray which supports it for its whole
length.
This tray is supported by a hinge bracket, called the coit-
sole, which, being fastened to the face of the breech, allows
the block and tray to be swung aside.
For such pieces the simple lever used in the field piece
affords insufficient power.
It is accordingly replaced by more or less complicated
machinery which, for the largest calibers, may be operated by
steam, hydraulic or electrical power.
One of the most ingenious devices is that of the French
engineer, Canet, who has an apparatus in which the contin-
uous rotation of a crank performs all the varied operations
of unlocking, withdrawing and swinging the block.
Vent.
The system adapts itself to the use of an axial vent which
facilitates ignition. To permit renewal, the vent piece is
* The latest model (1890) exhibits slight changes in the details of the
construction shown in figure 47, Chapter XV.
14 XXI. — VARIETIES OF CANNON.
made removable ; and to avoid erosion, its front portion is
of copper.
To avoid the danger of a premature discharge, the vent is
preferably protected by a sliding shutter, a projection from
which travels in a concentric groove in the rear face of the
piece which is so formed that the primer cannot be inserted
until the block is securely locked in place.
The complication attending the operation of an axial vent,
the likelihood of accident to the gunners from the projection
of the fragments of the ordinary primer and the necessary
delicacy of the safety shutter when made on the small scale
required for the field gun have so far caused these guns to be
provided with a radial vent piece of copper leading to the top
of the charge at about half its length.
Base Ring.
The seat of the block is of somewhat greater diameter than
that required for loading in order to give a large bearing sur-
face to the threads of the screw.
Under Barlow's law, this surface is less dilated by the gas
pressure than one nearer to the axis ; and, since from a simi-
lar reason the greatest stress is borne by the foremost fillets,
these do not approach as closely to the end of the tube as
the construction might otherwise permit.
All exposed screw threads have their angles rounded, to
avoid fracture and to resist deformation by the projectile in
loading. For heavy pieces a loading tray is slipped into the
opening so as to cover the thread in the base screw while the
projectile is being pressed home.
The operation of the gun is very much facilitated by de-
vices which avoid the translation of the breech block. One
of these consists in giving the breech block a general conical
shape so that it will swing directly into the position for
locking.
XXI. — VARIETIES OF CANNON. 16
The same end is accomplished in the Gerdon fermeture,
figure 13, now on trial in the United States. After revolving
the block through 90° so as to clear the two threaded sectors,
it is swung to one side through a slot cut in the jacket. A
radial slide on the rear face of the block acts both as a latch
and as a shutter to the axial vent.
The parts are remarkably few and simple.
Comparison of the Two Systems.
1. Except where metallic ammunition is employed the
French system permits the use of the best gas check.
2. It diminishes the weight of the gun for a given value
of u and d. Chapter XII.
3. It serves to press the cartridge into place instead of
guillotining it as in the Krupp.
4. The fermeture, when open, is less exposed to injury
from a front fire.
5. It may be worked by power.
The Krupp system in its conception is of almost rustic
simplicity.
This advantage is counterbalanced by the inferior gas
check which is required when non-metallic ammunition is
employed ; also by the thickness and mass of the forging
containing the slot, the presence of which must cause inju-
rious internal strain in oil hardening.
The jar in opening it suddenly may deform and even bend
the stop bolt. The parts are less securely protected in travell-
ing. It has also the comparative disadvantages named in the
discussion of the French system. The danger of premature
discharge, though not so great as in the French system, is still
said to exist.
16 XXI. — VARIETIES OF CANNON.
U. S. SYSTEM OF ARTILLERY.
MOUNTAIN SERVICE.
The Hotchkiss 1.65-inch Rifle.
This gun weight but a Httle over 100 pounds and its car-
riage about twice as much, so that either makes but a fair load
for a mule. Metallic ammunition is employed > The gun is
a single piece of steel provided with the simplest form of
Krupp fermeture as shown in figure 5 The operation of the
fermeture can be readily seen from the figure and from pre-
vious discussions.
Its special feature is the extractor, x. This is a prismatic
bolt, a hook on the front end of which engages with the
flange of the cartridge (Chapter XVI, figures 8 and 9) as this
is loaded
The extractor slides in a longitudinal groove, g, on the
upper surface of the slot On its lower face is a tenon which
enters a transverse groove, g' , in the upper face of the block.
The groove, g' ^ near the handle is straight and slightly
inclined to the rear face, so as to give power in wedging the
cartridge case from its seat. The screw thread on the latch
also assists. At the other end it is so curved that when, in
opening the breech, the loading hole comes opposite to the
chamber the extractor will be suddenly drawn backwards,
throwing the free cartridge case clear of the gun. The first
of these operations is called the extraction, and the second
the ejection
For simplicity this piece is fired with the ordinary friction
primer. The blast from this raises the central portion of a
thin, cup-shaped gas check within the cartridge, and the
flame passes through the three holes shown in figure 8, Chap-
ter XVI. As soon as the charge is ignited the back pres-
sure of the gases closes the vent by reversing the action of
the gas check,
XXI. — VARIETIES OF CANNON. 17
Hotchkiss 3-Inch Mountain Rifle.
In order to permit the use of shrapnel a heavier mountain
gun of 3-inch caUber has been recently produced. Figure 11.
Foreign Variations,
In order to increase both the power and portability of
mountain cannon they are frequently made abroad in sections
which are screwed together before firing. " Screw-guns " of
8-inch caliber have been successfully fired .
FIELD SERVICE.
The 3.2 B. L. Rifle shown in Chapter XV, figure 47, is
the only new field piece now issued. (1891.) It is eventu-
ally intended for use as a Horse Artillery gun, and to be
replaced for Field Service proper by a similar gun of 3.6
in caliber, firing a 20-pound shell. A 3.6 B. L. Mortar,
figure 12, firing the same projectile, is also contemplated for
delivering vertical fire against troops sheltered by temporary
defences. It has a range of nearly two miles.
Foreign Variations.
It is proposed in France to have but one caliber, about
3 in. for all mountain and field service, viz., short, light,
long and heavy pieces.
SIEGE SERVICE.
Siege cannon are intended for attacking and defending
inland fortifications and the land fronts of sea- coast fortifi-
cations.
The term is usually applied to pieces which, although too
heavy for field operations, are yet light enough to be trans-
ported over common roads upon the carriages from which
they are fired.
This limits the weight of the gun and carriage together to
that which may safely be transported across a pontoon bridge.
18 XXI. VARIETIES OF CANNON.
Siege Gun.
The 5-inch siege rifle, figure 6, resembles in its construction
the field gun described.
Siege Howitzer.
Principles of Design,
Defences of masonry have been largely replaced by those
which are armored, or, particularly for the besieging party,
of earth.
While armor requires for its penetration the concentration
of kinetic energy found in a projectile of relatively small
diameter fired from a gun, the demolition of earth works
demands rather the transfer of energy in the potential form.
Such defences should therefore be attacked by cannon of
the largest caliber consistent with portability.
If the maximum weight of the piece is fixed by the con-
siderations previously named, then by the definition of
Chapter I, a howitzer results.
The proportions of this piece are also demanded by the
advantages pertaining to vertical fire againt the large and
well defined area occupied by the besieged, against com-
munications of the besieger which are screened from view,
and against the roofs of turrets. The shorter the piece is
in rear of the trunnions the more easily may high angles
of fire from a given carriage provided with the ordinary
elevating screw be attained.* The avoidance of preponder-
ance and the requisite strength of the chase demand that
the length in front of the trunnions be also reduced.
Such considerations have fixed the value of u at about
12 times the caliber, which is 7 inches.
It is intended to throw a projectile weighing about 100
pounds to a distance of about 3 miles.
*A new German howitzer has the trunnions placed ahuost at the breech.
In this carriage the elevating screw is under the chase, as the arrange-
ment adopted gives a considerable muzzle preponderance. See also Car-
riage for 7-inch Howitzer, Chapter XXIII, figure 6.
XXK — VARIETIES OF CANNON. 19
Owing to the strength of the construction a larger cahber
might have been employed for the given weight, but in such
a case the energy. of recoil, (Equation 7, Chapter XIX,)
would have been excessive.
Since with the value of /„ usual in built up steel guns, the
short length of bore reduces the value of e^ it is proposed to
utilize the value of E permitted by the strength of the car-
riage by increasing the value of ;//.
This will permit the use of very long torpedo shells
(Chapter XVI, page 20). The limit of E for the wheeled
carriage having thus been reached, for high angles of fire
which increase the stress upon the axle, E may be further
increased by dismounting the wheels and laying the stock of
the carriage on a platform It is now (1891) proposed to use
in the field service a 6 inch B. L mortar throwing a 70
pound shell, to be mounted as above described
It is probable that in the future the obstruction to effi-
ciency which is due to the requirement that the piece be
transported on the carriage from which it is to be fired, will
disappear before the adoption of special carriages designed
with the view of efficiently satisfying their independent
requirements.
Charges.
In order to vary the angle of fall* to suit the range and
the kind of fire employed, the howitzer is fired with varying
charges of powder as well as with varying angles of fire. In
this it differs from the gun in which the charge is usually a
constant and a maximum. See Chapter XXX, page 9.
7-Iiich B. L Howitzer
The construction, figure 8, resembles that of the field piece,
the principal difference being in the construction of the key
ring. This consists of two semi-circular segments of rect-
*The angle with the horizontal made by the tangent to the trajectory
on impact.
20 XXI. — VARIETIES OF CANNON.
angular cross-section which are laid in a shallow groove in
the tube so as to project above its exterior and to bear
against the front face of the trunnion hoop. They are kept
in place by the lap of the sleeve.
The friction developed by shrinkage between the jacket
and the tube throws part of the longitudinal stress upon the
tube from which the key ring transfers this stress to the
trunnions.
A shoulder formed on the tube in rear prevents the for-
ward motion of the tube from the friction between it and the
projectile. See page 5. This feature is general,
The cavities in the ends of the trunnions are for the points
of the bailm which the piece is slung in mounting.
SEA COAST CANNON.
These comprise rifles of and above 8-inch caliber, and
12-inch rifled mortars,
Eifles.
Figure 7 shows the 8-inch b 1. steel gun with which most
of the recent experiments have been made.
The construction resembles that heretofore discussed,
except that the jacket is strengthened by two rows of hoops,
which since the original design, have been extended to the
muzzle. (Chapter XI, page 18, paragraph 4.)
Other S. C, Rifles.
The guns so far designed are of 8, 10, 12 and 16-inch
caliber. Being intended for use with the largest charges of
slow burning powder, they are made very long, the values of
u ranging from about 24 to 27 calibers.
For the largest calibers it is proposed to dispense with
trunnions which are to be replaced by several rows of cir-
cumferential ribs, by which, as in cannon of the very earliest
iimeSy the pieces are to be secured to their support. The
necessary alterations in elevation will be given by varying the
XXI. — VARIETIES OF CANNON. 21
inclination of the chassis, to which by this arrangement the
recoil is always parallel.
Mortars.
The importance of nearly vertical impact against the
decks of vessels at short ranges requires the mortars to fire
with angles of elevation as great as 75°.
It is proposed to group them in sunken batteries of 12 or
16 mortars, united under the control of one officer. He will
occupy a detached position free from smoke, and will be pro-
vided with an accurate range finder, and with means of com-
municating to the chiefs of pieces the direction and elevation
required. A simultaneous volley from the battery will prob-
ably drive from its anchorage any vessel within range. This
will be an important aid to the defense, since, as the bom-
bardment of Alexandria in 1882 clearly showed, the accuracy
of fire from a vessel is much diminished when the vessel is
under way.
V2,-inch B. L. Mortar. {Figure 9.)
The immediate supply of these cannon demanded by our
present necessities (1891) and the relatively low energies
required to penetrate armored decks by vertical fire have so
far permitted the body of these pieces to be made of iron
cast on the Rodman principle and strengthened by two rows
of steel hoops as shown in figure 9.
The recent failure at a pressure of less than 20,000 pounds
of an unhooped 12-inch cast iron mortar would indicate the
future use of steel throughout the piece as soon as the steel
works and the gun factory shall have become able to supply
a sufficient numl)er of heavy steel guns.
The growing importance of vertical fire has caused the
employment of mortars, even upon ship board, to be seriously
considered.
The value of u in this piece is about 6 calibers.
22
XXI. — VARIETIES OF CANNON.
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XXII. — ARTILLERY CARRIAGES.
CHAPTER XXII.
ARTILLERY CARRIAGES.
PRINCIPLES OF CONSTRUCTION.
Classification.
Artillery carriages may be classified according as they are
intended to support the piece when fired, to transport it, and
to supply it with ammunition and accessories. These func-
tions are sometimes combined.
They may also be classified according to the service in
which they are employed.
Requisites.
1. Strength to resist permanent deformation from the shock
of recoil.
2. Stability in firing and on the march.
3. Mobility as regards the ease of service in battery, and
of transportation when required.
4. Only a moderate recoil in firing, so as to facilitate the
service of the piece and to avoid the exposure of the gunners
when sheltered by defences. A compromise between these
properties is often necessary.
I. CARRIAGES WHICH SUPPORT THE PIECE.
GENERAL DESCRIPTION.
These are called gun carriages. They may be either sta-
tionary or wheeled.
Stationary Carriages.
The simplest form exists in the iron mortar bed used for the
old S. B. Mortars.
X3tll. — ARTILLERY CARRIAGES.
This consists of trapezoidal plates forming the cheeks^ which
support the trunnions of the piece at such a height as to per-
mit it to receive the elevation required. The cheeks are con-
nected by transverse diaphragms called transoms and bolts in
order to form a strong frame. For heavy pieces each cheek
may consist of two plates united to a T shaped bar as shown
in figure 1. The cheeks may be stiffened in the direction of
compressive stresses by bars included between the plates.
The bearings of the trunnions may be widened by trunnion
bed plates^ so as to diminish the pressure per unit of area
which they are called upon to support. The mortar bed is
made low for ease of loading and for stability. The prin-
ciples of construction above noted are of general application.
Sea coast gun carriages are intended to be used in firing
over a parapet or through an embrasure. In the first case
they are called barbette carriages, and in the second, casemate
carriages. Owing to the height of the piece above the
ground and the low angles of fire employed, the stability of
the system generally requires the support of the piece to be
divided into the gun carriage proper, constructed like the
mortar bed, and tlie chassis, which is a moveable railway
capable of directing the piece in its recoil and of being trav-
ersed in azimuth.
Non-recoil carriages are separately treated hereafter.
Wheeled Carriages.
In the mountain, field and siege services, the gun carriage
must also be adapted to transportation. This involves the
use of wheels, which complicate the problem of controlling
the recoil.
Parts.
Their essential parts are : —
1, The stock. This is a prolongation of the cheeks which,
with the wheels, forms the three points necessary for stability.
XXII. — ARTILLERY CARRIAGES,
A greater number of supports might affect the stability on
uneven ground.
The stock serves also to point the piece, since it sustains
the elevating screw, and with the aid of the handspike gives
the necessary changes in azimuth
It also connects the front and rear wheels in transporta-
tion.
For modern carriages the stock consists of two sheet
steel flasks or brackets which rest at the head of the stock
upon the axle, and are united at the further end by the trail
plate or shoe,
2. The wheels and the axle replace the continuous support
afforded in stationary carriages by the cheeks.
PERIODS OF THE RECOIL.
The recoil may be separated into two periods :
1, That during which the projectile is acquiring energy in
the piece.
2. That comprising the subsequent recoil. Since the
carriage is found not to move materially until the projectile
has reached the muzzle, and since the system is not rigid,
the corresponding phenomena may be taken to be :
1. A series of shocks between the trunnions and their
beds transmitted through the axles to the wheels and through
the stock to the trail. The system is finally set in motion by
these shocks.
2. The resulting motion of the system accelerated by the
remaining gaseous pressure and retarded by friction and
various artificial resistances.
Energy of Recoil.
The nature of the recoil is preferably studied by veloci-
meters of Class III. But, as this is difficult and requires the
previous construction of the carriage, it is customary for
theoretical discussions of a general nature to ignore the first
XXII — ARTILLERY CARRIAGES.
period, and to assume that the system is rigid and that the
acceleration to the system during the second period is com-
pensated for by the acceleration of the projectile noted in
Chapter XI, page 18.*
We may therefore change Equation (7), Chapter XIX,
to read
in which the subscript s refers to the entire system recoiling.
For greater accuracy, when the mass of the powder, or
m'^ bears a considerable ratio to that of the projectile, we
may use the following formula in which v' represents the
mean velocity of the products of combustion, found by
experiment to be about 3,000 /. s.
_ m V + m' v'
Distribution of "Work of Eecoil.
Since this work is distributed between the two periods,
and since it is necessary to restrict the exent of the recoil, it
becomes necessary, as in Chapter V, to determine the
maximum stress which the system can safely endure and to
maintain this stress as nearly constant as possible over the
path of the recoil.
This principle, which underlies all recent improvements, in
gun carriages, owes its importance to the recent increase of
m and e and the decrease m M (Equation 7, Chapter XIX),
due to the general use of built up rifled cannon firing large
charges o^ progressive powder In fact, it may be said that
the limit of the power of cannon, or h, page 21, Chapter XI,
is fixed by the difficulty of controlling their recoil,
If we assume that the mobility of the system fixes the sum
of the masses, M and J/', composing the gun and carriage,
This assumption will be corrected as occasion arises hereafter.
XXII. ARTILLERY CARRIAGES.
the following discussion explains the prevailing practice of
making M' approximately equal to M.
For, if we assume the carriage to be properly proportioned,
general experience shows that its permanent deformation, Q,
may be considered inversely proportional to its mass and
directly proportional to the energy which it receives. So that
liM-{- M' =z C, Q will be least when M — M'.
The assumption on which this deduction is based, although
confirmed by experience in the construction of carriages, an-
vils and armor, is not conclusive ; since mechanical ingenuity
may compensate for the loss of strength resulting irom a
diminution of M' .
REMARKS.
It is found that with quick powders the velocity of recoil
during the first period is greater than with slow powders, the
maximum momentum of the projectile being the same.
With slow powders the velocity during the second period
is increased to such an extent by the high pressure as the
projectile leaves the gun (Chapter XI, page 18), that special
devices have become necessary to diminish the increased
extent of the recoil.
The problem is so complicated that computations, princi-
pally by graphical methods, are mainly resorted to in order
to determine the direction of the stresses, the corresponding
dimensions being found empirically. It is highly probable
that the gun carriages of the future, like many other construc-
tions, will be the outgrowth of practical experience.
FORCES ACTING ON A GUN CARRIAGE.
Velocity of Translation.
If the axis of the bore intersects the axis of the trunnions
at the centre of gravity of the piece, the force producing re-
XXII. ARTILLERY CARRIAGES.
coil is communicated to the carriage at the trunnion beds.
The carriage being constructed symmetrically with regard to
the axis of the piece, we may suppose that the wheels, trun-
nion beds and trail are all situated in the same plane and that
the force producing recoil is applied at the point where the
axis of the trunnions pierces this plane.
The direction in which this force acts will be that given by
the angle of fire or the inclination to the horizontal of the axis
of the piece.
Let V figure 2, be the position of the axis of the trunnions,
and mv-=.I,^ represent the intensity and direction of the
force, and Q the angle of fire. Let Z'be the point of contact
of the trail and ground, / the distance of this point from the
trunnions, and a the angle made by the line Tv, with the
horizontal. Let W^ be the weight of the system acting
through the center of gravity G at the horizontal distance b
from the point T. Let/ be the coefficient of friction between
the carriage and the horizontal platform on which it rests.
The vertical component of /, , and W^ will cause friction
between the carriage and the platform. The force of friction
or/(^g 4" '^^ ^ s^'^ ^)' wil^ oppose motion. So that, repre-
senting by Fthe horizontal velocity of recoil, we have
y. m V cos 6 — / ( ^8 4~ ^^^ ^ sin B)
m V (cos — / sin 0)
in which g f may be neglected.
The vertical component will be distributed along the sup-
ports in a manner determined by the construction of the car-
riage and the values of Q. For wheeled carriages /will have
separate values for the wheels and the trail.
If, in Equation 4, we neglect the weight of the system in
comparison with the vertical component of 7, , (or g /), we
XXII. — ARTILLERY CARRIAGES.
find that V will reduce to 0, or that recoil will cease for a
value of 0, such that, calling this angle 0,
tan e, = y (5)
This is called the angle of no recoil.
Extent of Recoil.
The extent of the recoil will be
s=^-^.' (6)
If, as is usual, the platform be inclined at an angle, /3, with
the horizon so as to check the recoil, then for 6 in the above
equations should be written
d + (3; and for F, Tcos 3.
In this case, since the energy of the recoil is absorbed not
only by friction but by the work done in lifting JV^ through
a height = s sin (3, we have
Fcosfi'
2 g (sin (3 + / cos (i)
(J)
These equations are said to give correct values for stationary
carriages, but do not apply very exactly to those which are
wheeled.
Angpilar Velocity.
The force, /, , also acts to rotate the carriage around
the point T with a moment proportional to its lever arm,
/ sin (a — 6), so that the moment of this force will be
m V Isin (a — 6).
This is opposed by the moment of the weight, or JV^ b.
Then, since the angular velocity of the system is equal to
the resultant moment of the impressed forces divided by the
moment of inertia of the system, we have, representing the
XXII. — ARTILLERY CARRIAGES.
angular velocity, about T by o) and the corresponding radius
of gyration by k.
mvl sin (a — Q\ — W^ b
--S '-j^J •- (8)
With this relation we may discuss in an elementary manner
the stability of the system. For example, in the old S. B.
Mortars, since W^ is small, a is made less than 0, so as to
make w negative.
Phenomena of Recoil.
Practically the phenomena are much more complex, since
the rotation of the system is not immediate.
Wheeled Carriages.
In these the wheels tend to slide or rise to an extent
determined by the resistance to sliding at T. Since T is
not necessarily on a reciprocal axis of spontaneous rotation,
the stock is subjected to a transverse stress. When, after
rotation, the wheels fall, the axle receives a shock, and the
trail being thrown up, the system recoils by roUing, and so
on until the system comes to rest.
Rotation during the first period tends to derange the aim
by what is called the angle of jump^ See Chapter XX.
During the first period, since the trunnions fit rather
loosely in their beds, a frictional moment is developed on
the under side of the trunnions This causes abnormal
pressure on the head of the elevating screw, which, owing
to the elasticity of the system, subsequently receives one or
more severe blows from the breech. The effect is destructive,
since the bearing of this screw upon its nut is restricted, and
the necessary play between the screw and nut increases the
striking velocity of the parts.
The objections may be mitigated by making the piece
without preponderance, and by arranging the elevating screw
so that its axis will be always normal to the surface which it
XXII. — ARTILLERY CARRIAGES.
supports, since this will avoid the tendency to bend under
pressure.
Other phenomena also occur.
The inertia of the wheels develops in the axle a consider-
able transverse stress.
In rifled pieces a rotary moment is developed which tends
to raise from its bed the trunnion toward which the top of the
projectile is revolving, and thus to raise one wheel higher
than the other as the system jumps. The effect will be to
concentrate most of the shock of the fall upon the lower
wheel.
Stationary Carriages.
The chassis of stationary carriages revolves around a massive
vertical pintle which may be placed in front of the chassis or
at its middle.
While the former position is necessary for pieces firing
through embrasures, in other cases the center pintle chassis
is preferred, since a given change in azimuth covers less
ground.
The tendency of the top carriage to jump is restrained by
projections which engage under the chassis, but tend to lift
the pintle from its socket. The pintle is also exposed to a
horizontal stress nearly equal to the normal pressure between
the carriage and the chassis multiplied by the sine of the
inclination of the chassis to the horizon.
The strength of the pintle and its fastenings is therefore an
important subject of consideration.
Angle of Greatest Recoil.
Since the energy of recoil is distributed between the
motions of rotation and translation, the maximum velocity
of recoil will follow from an angle of fire such that w = 0.
Equation (8) does not contain all the data necessary for a
10 XXIi. — ARTILLERY CARRIAGES.
full discussion ; but it may be shown that, if the weight of
the system be neglected, and the notation of figure 2 be
adopted, if we call the angle of greatest recoil, 6^, then
Since A'^/i, this value of B^ is always positive, or the
maximum velocity of recoil will follow the use of an angle
of fire ]>0. This value of 6 should therefore be employed
in all calculations relating to limiting the extent of recoil.
The angle 6^, may also be called the ang/e of no rotation^
i. e. the angle for which all the energy of recoil is expended
in translation only. It may be taken to measure the exposure
of the system to the injurious shocks resulting from rotation,
since, in ordin-ary firing, Q is less than Q^^ and therefore rota-
tion is ordinarily produced.
Equation 9 shows that d^ may be diminished by the fol-
lowing means :
1. By making h' — h as small as possible. Owing to the
length of a in stationary carriages this correction is princi-
pally confined to those that are wheeled. In these h' is
made as small as facility of loading and the protection of the
gunners by the parapet will permit, and h is increased by
bringing the axle as near to the trunnions as the size, strength
and weight of the wheel will allow.
2. By making a as long as conditions relating to mobility
in transportation will permit. ,
3. By making /small.
In stationary carriages / is normally great, and, as here-
after seen, the resistance to sliding is generally artificially in-
creased. For these carriages it is especially necessary that a
be made large.
The stresses developed in field carriages by a large value
of/, as when the site is sandy or the trail is rested against a
XXII. — ARTILLERY CARRIAGES. 11
rock, are evidently prejudicial. They may sometimes be in-
evitable, as when firing across a valley at a high mark, since
in such a case the trail may require sinking into a hole.
DEVICES TO CONTROL RECOIL.
These may be considered according to the end in view,
as they seek, I, merely to limit the path; or, II, to regulate
the resistance.
It is generally advisable to store up enough of the work of
recoil to assist in bringing the piece back into battery. The
return may be facilitated by the use of eccentric rollers.
These devices ar-e often combined in the same carriage.
Class I. To the first class of devices belong those in which
the energy is absorbed by friction or in which a weight is
raised.
Stationary Carriages.
Friction Checks.
This variety is least valuable since it stores up no useful
work. In the best types the friction, due to the normal com-
ponent of the weight, is increased by the artificial pressure
of a screw clamp.
The effect of a given pressure on the screw may be in-
creased by increasing the number of surfaces upon which it
acts. Thus, in Ericcson*s compressor we have 7i parallel plates
attached to the chassis and alternating between n -\-l pieces
so attached to the carriage that while they recoil with it, a
sHght initial play is allowed. Suppose this play to be de-
stroyed by a normal pressure P. We shall then have for the
friction of the compressor P =: P/ {2 n) and from Equa-
tion (7)
(v cos 13 y
2g(s[nf5+/cos(3+-^j
(10)
12 XXII. — ARTILLERY CARRIAGES.
The main objection to this system is the variable value of
F^ since this depends upon the judgment of the operator, and
upon the state of the surfaces, and is greater for static friction,
when the acceleration is greatest, than afterwards.
This arrangement is modified in the Sinclair check used
with some converted U. S. Sea Coast guns.
This consists essentially of a clamp embracing a plate in-
creasing slightly in thickness from front to rear. To prevent
the plate from buckling in consequence of the counter recoil
produced by the elasticity of the parts, the front end of the
plate is free to move forward through its attachment to the
chassis.
Wheeled Carriages.
These may be braked by various means. Among these is
the Hotchkiss brake which consists of nuts threaded upon the
axles between the wheels and serving, by friction produced
against the hubs of the wheels, to keep the wheels from
turning.
This brake is an example of the friction clutch often em-
ployed in the transfer of energy. When the tangential com-
ponent of the force producing rotation exceeds that of fric-
tion, sliding takes place and the destruction of the resisting
parts is averted.
This principle is sometimes applied to the elevating screw,
since the clutch, which is required to vary d only, will
yield under the shocks of recoil and save the deformation
of the parts.
A simple brake may be extemporized by lashing the
wheels to the trail by a rope ; but, as this strains the wheel,
a better way, often used, is to rest the wheels on shoes
attached by tension to the trail, as in wagons of commerce.
The latest patterns of brake admit of a partial distribution
of the pressure, as explained later and in Chapter XXIII.
XXII. ARTILLERY CARRIAGES. 13
They may also be used in transportation without necessarily
stopping the carriage, as is required when the shoe is used.
Raising a Weight.
If the piece raise its own weight, its exposure is increased ;
while, if it raise a counterpoise, it may itself descend. Such
carriages are called disappeari7ig carriages,
Moncrieff Carriage. — Figure 3
In this the flasks rock on the chassis so that the counter-
poise, Wy which was at first beneath the gun, has finally
a considerable moment of restitution. By varying the
curvature of the flasks this moment may be made to vary
inversely with the acceleration of the recoil so that the
stresses between the piece and the counterpoise may be
nearly constant. Conversely, the return to battery will be
gentle. The rack and pinion serve to retain the piece for
loading, and to control its return to battery.
Kings Carriage.
The chassis is steeply inclined to the rear, and the coun-
terpoise, which is in a well, is lifted by a rope passing
through the pintle.
This carriage, invented by Major King of the Engineers,
is cheaper than the Moncrieff", and has been successfully
tried in the United States.
In both carriages exposure may be minimized by aiming
with mirrors, and by firing by an electrical contact automat-
ically made when the piece comes into battery.
•
Regulation of Stress.
1. BY FLUID PRESSURE.
The method now generally adopted is the use of hydraulic
or pneumatic buffers.
14 XXII. — ARTILLERY CARRIAGES.
These consist essentially of a cylinder and a piston, rela-
tive motion between which results from the recoil. The
effect is to force the fluid contained in the cylinder through
orifices or ports which may be either constant or variable
in size
In the pneumatic buffer the ports are in the cylinder heads ;
in the hydraulic buffer, as the liquid is to be used again, they
are in the piston.
Pneumatic Buffer,
This, although simpler and requiring less attention than
the hydraulic buffer, is more bulky, can be less easily regu-
lated, and gives an injurious counter recoil.
Hydraulic Buffer,
Description. Let the arrangement be in principle such
as shown in figure 4. C is the cyUnder filled with a non-
freezing mixture of glycerine and water ; it is attached to the
carriage P is the piston fixed on the rod R^ which is secured
to the chassis.
Many alternative arrangements are made.
By placing it under tensile stress during the recoil, the
bending of the rod may be avoided.
The size of the ports in the piston may be varied by the
profile of the ribs, r, which are fixed to the interior of the
cylinder, or by a notched disc revolving on the piston and
provided with projections which enter rifle grooves in the
cyhnder.
We will consider only the second period of recoil, and will
neglect the friction of the liquid and that of the rod in its
stuffing box, so that the pressure considered "^ill be that
required to give a constant acceleration to the fluid.
The value of this method appears from the fact that it may
safely restrict the most powerful cannon to a recoil of about
3 calibers.
\
XXn. — ARTILLERY CARRIAGES. 15
Notation, ,
Let:
A be the area of cross-section of the bore of the cylinder
diminished by that of the piston rod and ribs.
a^ the total initial area of the ports.
a this area at the end of the time, /, or after a displace-
ment, X.
v' the corresponding velocity of the liquid current.
11 the corresponding velocity of recoil.
Vq the initial velocity of recoil, obtained either by meas-
urement or by means of the formula
("'+?)
.„- ^_ r;[cos(e, + /3)-/sin(9, + /3)] (11)
derived from Equation (9), Chapter VII, and the remarks
noted on pages 7 and 10 herein.
6 the density of Uquid, or the ttiass of one unit of its
volume.
P the pressure on the piston at any moment.
a the corresponding acceleration.
Extent of recoil. If the cylinder is full, the volume a v',
of liquid which in a unit of time passes from in front of the
piston to the rear must be equal to the volume, A u caused
by the translation of the cylinder, whence
Au
(12)
The
mass of the
liquid
escaping in
the
time
A/
is then
;;/ =
8av'
A/= 6 A u
A/
(13)
and its
energy
mv"'
6 A' u'/\ t
-
a4)
2
- 2d'
16 XXII. — ARTILLERY CARRIAGES.
This is equal to the work done by P over the path u A /,
and therefore
„ d A" u^
Since P is constant, Equation (15) must be true, for the
initial values of u and a, and therefore
From this, by equating the initial energy of the system,
with the work of the resistances, including the lifting of the
weight of the system, and the work of friction over the path
iS", we have
~\^^^\_~2^' +^-^s(sin/3+/cos/?)J, (17)
from which S can be determined when A and a^ are known,
or from which a^ can be determined when *S and A are
known.
Profile oj the ribs. From the theory of energy we have
or
u=K^l-^-^ (19)
Also, since the recoil is uniformly retarded if we consider
the resistance of the liquid only, we have
Fl = 2a S
which value of VI in Equation (19) gives
«=K\/i-i-
which from Equations (15.16) may be written
-V^
(20)
(21)
XXII. — ARTILLERY CARRIAGES. 17
a
If there are n similar ports, the area of each one is - -. If
n
each notch in the piston has a breadth, b^ and a depth, d^
and the rib has the same breadth and, as shown by figure 4,
a variable depth, j, then
a = nb {d — y) (22)
Which value of a substituted in Equation (21) and solved
with respect to y gives
This is the equation of a parabola.
At the end of the recoil, when x = S, y =z d, or the ports
are completely closed
This formula applies only to the path of the recoil after
the system has acquired its maximum velocity or during the
second period.
While the projectile is in the gun the piece recoils from one
to two inches and continues to gain velocity for four to six
inches more so that the maximum velocity is not attained
until after a recoil of five to eight inches
Figure 11 shows these phenomena and the effects of a
suitable control, based largely upon the analysis of velocity
curves obtained during the practically free recoil of the ])iece.
The data were as follows : Weight of piece, about 100000
lbs. ; of projectile, 754 lbs. ; of powder, 244 lbs. ; initial
velocity, 1857 f. s.
Cylinder, The thickness of the walls of the cylinder may
be determined from Equation (4), Chapter XIX, by placing
The area A will be determined practically by the construc-
tion of the chassis. As the depth of the chassis limits the
18 XXII. — ARTILLERY CARRIAGES.
diameter, it is customary to have two cylinders connected by
a tube so as to equalize the resistances and prevent slueing.
Counter RecoiL Owing to the incompressibility of most
liquids the tendency to counter recoil is slight ; and, as the
velocity of return is small, the weight of the system generally
suffices to return it to battery.
Or the hquid may be forced into another vessel or a set of
stationary vessels containing air or powerful springs, which
store up energy to return the piece to battery when a valve
or latch is opened. Figure 5 illustrates the operation of such
a carriage. When air is compressed by the liquid, the variety
is known as the hydro-pneumatic
Regulation of Stress.
2 BY THE ELASTICITY OF SOLIDS.
The weight of the cylinder, and the difficulty of prevent-
ing leaks in the preceding apparatus, renders it objectionable
in wheeled carriages, and more so for those used in the field
service than for those in the siege service
A compromise has therefore been sought by the inter-
position of an elastic solid, the work done upon which in the
first period will reduce the shock felt by the system. The
restoration of this work is not essential, although it tends to
distribute the stresses over the path.
Such an arrangement is shown in the Engelhardt (Russian)
carriage, figure 6.
Engelhardt Buffer. The flasks are notched so as to allow
the axle, a^ a limited play. They are also similarly pierced
for the cross-bar, ^, each end of which is united to the outer
end of «, by a brace, k. This keeps the axle from bending
easily since the force of recoil is applied close to the wheels.
The transom, c^ separates e from an elastic buffer, K The
buffer consists of layers of cork, rubber, or of Belleville
XXII. — ARTILLERY CARRIAGES. 19
Springs {post ), assembled on a bolt, /, the front end of which
is secured to e, and the rear end of which is provided with a
nut, d.
When discharged, the piece, with its flasks and c and b,
slides back relatively to the wheels and / and ^, so that b is
compressed. A considerable proportion of the energy of re-
coil is thus absorbed before the wheels begin sensibly to move.
After recoil, the elasticity of b restores the parts.
Belleville Springs, These are saucer shaped discs of sheet
steel, pierced by an axial hole by which they are united in
pairs on a spindle, base to base. They are now much used
under compression where space is limited.
Lejnoine Brake. The French artillery have borrowed from
the omnibus of Paris a more perfect but more complex brake,
figure 12. On the march it may be set against the tire, by
hand, as in the wagons of commerce. When the piece is
fired, the relative motion of a mass, w, throws forward the
elastic cross-bar, b^ to each end of which is attached a taper-
ing cord, c. Each cord after making several loose turns
around the nave is secured to the brake beam, B. When m
is thrown forward it is held in place by the serrated edge of
an axial bar, b', to which it is secured. The motion of b
stretches the cords and tightens them around the naves so
that they are further wound up by the revolution of the
wheel in recoiling.
The greater the extent of the recoil at any instant, and
therefore the less the velocity of recoil, the thicker will be
the cord and therefore the greater will be the increment of
the pressure of the brake upon the tire.
See also the U. S. Buffington brake in the next chapter.
PLATFORMS.
To insure continued accuracy of fire from the same site,
it is absolutely necessary that the carriage should rest upon
a solid and substantial platform,
20 XXII. ARTILLERY CARRIAGES.
The mobility of field pieces restricts this necessity to the
sea coast and siege services.
In the sea coast service the platforms are constructed by
the Engineer Department with the works which the cannon
defend.
Wooden platforms are employed for siege pieces, in which
long continued firing at one object as in breaching, would
cut into the unprotected soil deep ruts, which would increase
the difficulty of serving the piece and restrict both its
horizontal and vertical field of fire.
The construction of the platform should be such that it
may be taken up without injury for removal to another site.
Siege platforms consist of a certain number of pieces of
wood ; and in order that these pieces may be carried on the
backs of soldiers from the depot to the battery, the weight
of the heaviest piece should not exceed fifty pounds. Siege-
platforms consist of sleepers (i), (fig. 7), and deck platik (2).
The general direction of the sleepers is parallel to the axis
of the piece, and the deck-plank at right angles to it ; this
disposition of the parts offers the greatest resistance to the
recoil of the carriage. The deck-planks are fastened together
at their edges by dowels ; the outer planks are secured by
iron eye-pins, one at each end of a sleeper. The platform is
secured in its place by driving stakes around the edges.
There are two principal platforms for the siege-service, viz.,
the ^2^;z-platform and the mortar-'^XdXioxm. The former is
composed of twelve sleepers and thirty-six deck-planks; the
mortar-platform of six sleepers and eighteen deck-planks.
A simple and strong mortar-platform, called the rail-
platform may be used where trees or timber can be easily
procured. This is composed of three sleepers and two rails,
secured by driving stakes at the angles and at the rear ends
of the rails. The rails are placed at the proper distance
apart to support the cheeks of the bed.
XXII. — ARTILLERY CARRIAGES. 21
II. TRANSPORTATION.
For certain light pieces, as machine guns, a two-wheeled
vehicle is used. Where the weight of the load requires its
distribution on several supports, the gun carriage is converted
into a four-wheeled carriage by attaching it to another two-
wheeled carriage, called the limber.
PRINCIPLES OF THE WHEEL.
In transportation the wheel is intended to transfer sliding
friction from between the surfaces of the tire and the ground,
where the coefficient of friction is large and variable, to the
lubricated surfaces of an axle and its bearing, where the
coefficient is small and nearly constant.
In this respect its value as a mechanical power varies
directly with the radius of the wheel and inversely with that
of the bearing.
The wheel, as shown by figure 8, increases also the lever
arm, /, of the power, P, with respect to that, q, of the weight,
W^ to be raised over the obstacle, h.
On these accounts, since the diameter of the bearing,
which is generally equal to that of the axle arm, is fixed by
the maximum stress which the axle arm has to support, the
mechanical advantage of the wheel increases with its diameter.
An increase in diameter as well as in the width of the tire,
diminishes the pressure per unit of area between the tire and
the ground, and therefore diminishes the rolling friction, or
the work lost in permanently deforming the ground on which
it travels. The elasticity of the wheel also favors this reduc-
tion ; hence the use for railways of iron wheels on iron
tracks.
The increase in size is limited by the weight of the wheel,
the stability of the system on the march and in firing, and the
convenience of loading. The mobility of transportation
also limits the size, for all wheels in the same service being
22 XXII. — ARTILLERY CARRIAGES.
interchangeable, the facility of turning depends upon their
diameter, as will be shown.
As shown by figure 8, an advantage also follows from
inclining the direction of the draught, particularly for the
front wheels, which do most of the work of rolling friction
and which therefore are designed to carry only about J of
the total load. Since the point at which the horse exerts his
power is fixed by his conformation, it is evident that this
advantage will be diminished with the increase of diameter of
the wheel.
These considerations have generally fixed the diameter of
all field artillery wheels at about 5 feet, and their weight at
about 200 pounds.
Siege wheels are made heavier and larger.
CONSTRUCTION OF THE WHEEL,
The requisites of size, weight, elasticity and facility o. re-
pair demand a more general use of wood in the wheel than in
other parts of the carriage, and involve a marked application
of the principle of independence of function. This will ap-
pear by comparing the rudimentary wheel, still used in remote
districts, consisting of a disc cut from the trunk of a tree, with
the complex elastic structure employed in the bicycle.
The Archibald wheel, figure 9, now much used in the U. S.,
resembles that now generally employed in other services,
although it applies less fully the principle above named.
Starting from the center, which is the best way of consid-
ering any circular structure, we find : — N^ N\ the 7iave or
hub. This receives the pressure of the axle arm on a lubricated
surface, and distributes the pressure to the spokes. The nave
is made in two parts, to facilitate repairing the spokes. The
portion of the nave in contact with the axle, or the axle box,
is so shaped as to receive the lubricant in the cavity, O,
XXII. ARTILLERY CARRIAGES. 23
In some foreign wheels and in the ordinary wooden wheel
the axle box consists of a separate piece, so that it may be
replaced when worn. Since friction is less between dissimilar
metals than between surfaces of the same metal, and in order
to cause the wear to take place most on the part which can
be most easily replaced,* the axle box, when separate, is pref-
erably made of phosphor-bronze, while the nave, as in the
Archibald wheel, may be made of malleable cast iron. The
metal nave marks a great improvement over the wooden nave
formerly employed. The cross section of this piece made it
difficult to season, its softness caused it to wear from the
alternate compression of the vertical and extension of the
horizontal spokes, and it was especially exposed to decay
from moisture lodging in the angles between the spokes.
6", 6", are the spokes, which transmit the weight to the rim.
For elasticity and facility of repair they are made of oak or
hickory. Their inner extremities are shaped like voussoirs,
which abut closely upon the box to avoid destructive play.
In the Archibald wheel the voussoirs are made a trifle large
and simultaneously set together by a powerful radial press
which subjects them to a stress many times greater than they
are likely to receive in service.
R is the rmi which distributes the weight over the ground.
For the same reasons as the spokes, and because mud adheres
less to wood than to iron, the rim is made of oak. In order
to avoid cutting too much across the grain the rim consists
of a number of segments called felloes or fellies.
T is the tire, shrunk on to bind the parts together and to
protect the rim from wear. As it may require shortening in
order to produce the necessary compression on parts which
have become loose from wear, it is usually made of wrought
iron or of low steel.
*This is an important principle in machine design.
24 XXII. — ARTILLKRY CARRIAGES.
The figure shows also various bolts and clips and the
line h pin and ivasher, the functions of which are evident.
Dish.
The spokes are so arranged as to form a conical surface
which is called ih^dish. The principal object of the dish is
to give stiffness to the wheel, since (figure 13) on a trans-
verse slope or on uneven ground, the lower wheel, which
bears the greatest share of the weight, will resist the lateral
thrust of the axle by a compressive stress upon the spoke.
If the spokes lay in the plane of the rim, there would be an
alternating transverse stress on the ends of the spokes ; this
stress would make them work loose in their sockets and accel-
erate the destruction of the entire machine.
Axle.
T\ie axle or axle tree consists of the body and the arms.
The arms are conical so as to give the greatest strength with
the least mean diameter. In some vehicles, the wear between
the arm and box is taken up by means of washers of varying
thickness.
The axis of the arm is inclined slightly downward, forming
the hollow^ and to the front, forming the lead. Both together
constitute the set of the arm.
In a dished wheel the hollow frees from transverse stress
the *' working spoke," which is that which bears the greatest
load ; it also relieves the linch pin from thrust. For a given
width of carriage body it allows the axle body to be made
shorter and therefore stronger ; and, from the inclination of
the plane of the rim, it tends to throw the mud clear of the
carriage.
The efiect of the lead is to diminish the transverse stress
upon the front spoke in meeting obstacles.
XXII. — ARTILLERY CARRIAGES. 25
Axle Body.
Although the interval between the cheeks transfers the
transverse stress upon the axle to points near the wheels, it
was found necessary in former carriages to reinforce the axe
with a wooden body. In modern carriages this is sometimes'
replaced with two grooved plates which clamp the cylindrical
axle between them and are extended to the front and rear so
as to stiffen the axle in recoihng. They also serve to fasten
the axle to the cheeks. The axle may, without sensible loss
of strength, be made hollow, and three-fourths of its weight
when solid.
THE STOCK.
The prolongation of the cheeks is called the stock. The
use of metal instead of wood, has permitted a return to the
construction of the great French designer. General Gribeau-
valy in whose gun carriages the flasks were parallel extensions
of the cheeks.
The metallic flasks now used converge to the trail.
In the stock trail syste?n, recently in use, the cheeks con-
tained between them a single piece of wood called the stock.
Besides its functions under fire the stock of the gun carriage
unites the two axles of the four-wheeled vehicle, as does the
reach or perch of the ordinary vehicle. For artillery carriages
used simply for transportation, such as the caisson and the
forge, the stock is a single piece of wood joining the body to
the limber.
Tiirnmg A?igle.
The dimensions of the stock affect the mobility in turning.
This is often measured by the tiirfiing angle, which is half the
horizontal angle through which the pole can revolve when
the carriage is at rest. Practically, the space required to turn
the carriage will vary with :
1. The length and width of the line of horses and their
gait.
26 XXII. — ARTILLERY CARRIAGES.
2. The distance of the pintle from the vertical plane tan-
gent to the rear face of the front wheels.
3, The thickness of the stock at the point rubbed b" the
wheels in turning.
• 4. The length of the stock.
Owing to the first condition above named a turning angle
of 60° is generally considered as sufficient. This may be
increased by increasing the distance of the pintle from the
front axle, but this is apt to cause the pole to *' thrash."
Pintle.
The distance of the pintle in rear of the axle in connection
with the moment of the trail, afiects also the pressure on the
necks of the wheel horses caused by the moment of the pole.
In siege carriages and in those used only for draught, the
pintle is placed at some distance to the rear ; or a similarly
placed transverse sweep bar is used, which supports the
weight of the stock.
But, in field carriages for which flexibility of attachment
and mobility are essential, the pintle is placed more to the
front and the evil corrected as far as possible by distributing
the load or by various mechanical means.
In this arrangement the preponderance of the system com-
posed of the gun and its carriage is an important factor. If
the trunnion beds are moved towards the Hmber the pole is
lifted, but the labor of Hmbering is increased, and the sta-
bility of the carriage in firing is diminished. (Eq. 9.)
To diminish the labor of limbering, the pintle is placed as
low as permitted by the requirement that as much free space
as possible should be left beneath the axles for mobility on
ground covered with large stones, stumps, etc.
In the siege service, as the piece does not require to be
brought into action rapidly, and as the limber carries no
extra load, the piece may be shifted to the traveling trunnion
XXII. — ARTILLERY CARRIAGES. 27
beds which, on the march, are in front of those from which
the piece is fired.
THE LIMBER.
Nomenclature.
The wooden field Umber, figure 10, is composed of an
axle tree (1) ; a fork (2) ; two hounds (3, 3) ; a splinter bar
(4) ; two foot boards (5, 5) ; a pole (6) ; the pintle hook and
key (7); two pole yokes (8, 8); and pole pad {^).
Ahhough destined to be soon replaced by one composed
more largely of steel, it is here discussed as it illustrates some
valuable principles-
The hounds serve to support the ends of the limber chest
and the foot boards, and also to transmit the draught of the
horses from the splinter bar to the axle.
The pole or totigue is employed to stop the carriage and to
give it direction. As it is liable to be broken, it is practically
made in two pieces, of which the fork, which is least exposed
to accident, forms one. The fork then is a socket for the
pole, and braces the entire frame by its attachment to the
axle body and the parts in front.
The pole should be so attached to the fork that it may be
readily replaced when broken.
The pole yokes transfer the weight of the free end of the
pole to the necks of the wheel horses and the soft pad pro-
tects the leading horses from harm.
Attachments,
The metaUic limber body consists of channel irons and T
angle irons united in various ingenious ways. The rigid
splinter bar may be replaced by the ordinary jointed double
tree and si?tgle trees. These permit the horses to work more
independently of each other than the splinter bar does, but
are probably not so strong. A joint is always a cause of
expense and generally a source of weakness.
28 XXII. — ARTILLERY CARRIAGES.
In the British service the pole is replaced by shafts.
Since the pace of the team is regulated by that of the slowest
horse, this arrangement, while more manageable than the
pole, and therefore better fitted for the showy evolutions of a
drill, is objectionable for the march, since the work which
devolves on the shaft horse diminishes his endurance.
The Limber Chest
This serves to carry ammunition, and also furnishes a seat
for some of the cannoneers. The gun carriage is often
arranged to carry two cannoneers on side seats, in order to
diminish the time required for coming into action, a matter
which, owing to the precision, rapidity and range of infantry
fire, is becoming of vital importance. The carriage also
often carries two rounds of canister for use at close quarters.
The principal distinction between limber chests depends
upon how the lids are placed.
If on top, the chest may easily be made waterproof in
fording streams ; but the contents are less accessible. If
behind, the lid may form a convenient tray for preparing
fuzes, &c. This arrangement is more liable to accidental
opening than the former, and waterproof packages for the
cartridges may be necessary.
The ammunition chests in the U. S. Service are still con-
structed of wood. In other countries sheet steel is generally
used. For what reason is unknown ; since, if not unduly
heavy, they are not proof against infantry fire.
THE MORTAR WAGON.
This is used for transporting siege projectiles, mortars and
their beds, and spare guns.
The body consists of a strong, rectangular frame provided
with a stock by which it is attached to the siege limber. At
the rear of the body is placed a windlass which aids in loading
XXII. ^ARTILLERY CARRIAGES. 29
heavy weights. Stakes may be placed around the sides to
sustain boards used in retaining loose objects.
Since rifle projectiles are always issued boxed instead of
loose, as was the former custom, the necessity of the mortar
wagon for their transportation no longer exists; but its
general utility is great. It will .probably be used hereafter
for transporting siege guns for considerable distances, since
the height of the carriage from which they are now fired
renders them unstable on rough roads.
A special wagon with a crank axle, so arranged as to carry
the load close to the ground without diminishing the height
of the wheels would appear to offer special advantages.
III. CARRIAGES FOR SUPPLY.
New U. S. System.
These include, 1st, the caisson^ for carrying a larger quan-
tity of ammunition than can be carried by the limber, and
also a spare pole, wheel, handspikes, buckets and tools ;
2nd, the forge and battery wagon, containing a larger assort-
ment of tools and material for repairs ; 3rd, the artillery
store wagon, an ordinary four-horse wagon, containing extra
small arms and ammunition and the men's knapsacks, etc.,
so as to confine the load of the fighting teams to the neces-
sities of action.
REMARK.
The increased weight of each round of modern ammuni-
tion and the necessity for an even greater number of rounds
than formerly sufficed, increases the difficulty of supply.
It is proposed abroad to increase the number of caissons
per piece and to retain the supply in the limber for extreme
emergencies.
XXtil. — VARIOUS AkTiLLEkY CaRria6E§.
CHAPTER XXIII.
VARIOUS ARTILLERY CARRIAGES.
The U. S. Field Carriage. Figures 1-4.
Constmction,
This carriage, designed by Colonel Buffington of the Ord-
nance Department, is made of steel, since, owing to the large
value Qii h of this gun (Chapter XI, page 21), wooden car-
riages, and even some differently constructed of steel, were
found insufficiently strong.
The principal features relate to the construction of the axle
body, of the stock and to the operation of the brake. The
hollow cylindrical axle is strengthened by axle plates, figure
2, which stiffen it in the direction of the recoil. The stock
consists of two brackets, each of which is made of two nearly
symmetrical sheets of steel stamped hot between dies so as to
give the corrugated cross section indicated in figure 3. When
riveted through the webs, each bracket forms a strong, light
truss, resisting stress both in its own plane and transversely.
The lower flanges of the outer plates project inwardly and
serve to unite the brackets to the axle plates. The brackets
are further united by transoms, three of which with a hinged
lid form the trail box for the oil can and tools which have
become a necessary portion of the equipment.
The carriage is provided with two axle seats for cannoneers.
The wooden handspike is permanently hinged to the trail.
Elevating Screw,
The space between the brackets allows the breech to
descend sufficiently for the high angles of fire used with low
XXIII. — VARIOUS ARTILLERY CARRIAGES.
charges against troops sheltered, from view, and the crank
which operates the elevating screw is placed at the side, so
that under these conditions it will be readily accessible.
The nut of the elevating screw oscillates slightly on trun-
nions, and the head of the screw is connected by a fork to
an axis parallel to and beneath the trunnions, so that, as the
angle of fire changes, the axis of the screw will be nearly
normal to that of the gun.
Brake.
The great strength of this carriage has permitted the
employment of Colonel Buffington's brake, figure 4.
This consists of an [_ shaped rod, the stem of which is
surrounded by a spiral spring contained within a tube ; the
rod swings freely from a loose joint situated eccentrically
above the axle.
The length of the brake is such that when held vertically
the hook will pass over the wheel ; and, being allowed to fall
to the rear, it will engage with the tire at some point as a.
When the wheel revolves in the recoil, the friction at a
tends to extend the rod. But this compresses the spring and
increases friction, so that as the velocity of recoil decreases,
the resistance to rolling increases, and the retardation
a])proaches constancy, at least during the critical period
preceding sliding.
The recoil has thus been reduced from 26 feet to 8 feet,
without injury to the carriage.
In transportation the brake is secured vertically to one of
the seat arms. It may also be used as a traveUng brake.
Limber and Caisson.
These carriages are constructed substantially on the lines
previously named. Steel angle irons are largely used for the
frame.
XXIII. — VARI6US ARTILLERY CARRIAGES. 3
The chests, which are of wood, open on top and are only
high enough to receive the projectile standing ; this brings
the center of gravity very low.
The cartridges lie in a compartment between the two end
compartments reserved for the projectiles, which thus serve
to protect the powder from hostile fire.
For safety, no friction primers are carried with the powder,
as was formerly done. Unbroken packages are placed in
outside cases, and loose primers are carried with the tube
pouch in the trail box.
The four chests per piece can carry 42 projectiles each,
with a greater number of cartridges for curved fire.
The Siege Carriage. Figure 5.
The principal feature of this carriage is its height. For
the protection of the gunners the axis of the trunnions is
placed 6 feet above the ground.
In order to prevent the system from tipping forward in
limbering, the trunnions are so placed that when limbered
the center of gravity of the system will fall between the axles.
The wheels, axle plates and brakes are such as just
described.
The carriage is intended to transport the piece only for
short distances about the work which it defends.
REMARK.
A small hydraulic buffer connecting the stock with a pintle
sunk into the platform between the wheels, and two movable
chocks, assist in controling the recoil. The chocks rotate
around the pintle with the gun and serve to return the piece
into battery.
The Siege Howitzer Carriage. Figure 6.
The piece is mounted in two trunnion carriages, a, upon
the inclined slides, '^, upon which it is allowed a recoil of six
4 XXIII. — VARIOUS ARTILLERY CARRIAGES.
inches. The recoil upon the shdes is checked by the
hydrauhc cyUnders, r, and the courses of Belleville springs,
d. The latter serve to return the piece to the firing position.
They rest against the traveling trunnion beds, e^ and the rods
upon which they are strung pass through holes in these beds.
The flasks, /, are of rolled steel plate \ inch thick, and are
flanged inward except on their upper edges. From each
flask is cut a large triangular piece in order to diminish its
weight ; the edges of the apertures being flanged inward as
above. The flasks are xmited by three transoms, ^, and the
double transom, //, to which is fastened the piston rod of the
hydraulic brake.
The flasks rest upon the axle through two iron forgings, /,
and are strengthened by two supporting plates,/.
In order to facilitate the elevation of the piece a pecuhar
arrangement is employed. This consists of the elevating
rack, /, which is attached to the piece, and the worm, m ; the
shaft, ;/, and the hand-wheel, o. The worm is attached to
the right trunnion carriage, and in recoihng slides along the
shaft, n. A spline (see AVebster) on the shaft permits the
worm to shde along the shaft, and yet constrains it to follow
in any position the rotation given to the hand-wheel, o.
The advantage claimed from this design is that the recoil
of the piece upon the carriage so diminishes the maximum
stress upon the flasks and trail that their weight may be
greatly reduced. A portion of the weight so saved is used
to strengthen the axle and the wheels.
Weight of wheels, 375 pounds, each.
Weight of carriage, complete, 3200 pounds.
Pressure of trail on platform, 13(K) pounds.
Height of trunnions, 6 feet.
XXIII. — VARIOUS ARTILLERY CARRIAGES. 5
Barbette Sea Coast Carriage.*
The principal feature of the gun carriage is borrowed from
the old *' flank-defense howitzer" carriage.
Its object is to return the piece to battery and by diminish-
ing the variable work of sliding friction to increase that of
the hydraulic buffer, which can be made constant.
Each cheek carries two rollers ; that in rear is on an
eccentric axle and that in front is on a concentric axle.
When the piece is in battery the front rollers are nearly in
contact with the chassis rail ; while those in rear are usually
raised from it, but may be thrown in contact by means of the
eccentric. The lower front angles of the cheeks are trun-
cated, so that, when the carriage is thus tilted to the front, all
the rollers come into play and the piece may be moved from
battery with comparative ease.
In firing, the rear rollers are out of gear so that the vertical
thrust of recoil is borne by the lower face of the cheek and
the axles are not endangered.
As the carriage recoils the rear rollers strike inclined planes
bolted to the upper surface of the chassis rails and tilt the
carriage sufficiently to cause it to move by rolling until it
returns again to battery.
Muzzle-loading guns are retained from battery by means of
an automatic latch.
MODERN TYPES OF SEA COAST CARRIAGES.
Owing to our deficiency in modern cannon the U. S. have
not yet (1891) decided on any special pattern of sea coast
carriage; but the following examples, derived from the
French service, probably contain the essential features of the
system to be adopted for the barbette carriages, as soon as
the new cannon shall have been supplied.
* The Sea Coast Battery at West Point contains several specimens of
this type.
O XXIII. — VARIOUS ARTILLERY CARRIAGES.
The types of disappearing carriages and those designed
for turrets are too numerous for description here. They
generally apply the principles previously discussed with those
treated in the course of Military Engineering.
Gun Carriage.
Figures 7, 8 represent the elements of a modern sea coast
barbette gun carriage. It consists of three main parts : 1st,
the top carriage, T^ consisting essentially of the buffer; 2nd,
the chassis, C, the lower part of which is circular ; by means of
a great number of loose conical rollers, it revolves upon the
circular pintle platform, P. This platform, cast in a single
piece, rests upon a proper foundation.
To avoid the complications due to sliding friction during
recoil, the top carriage also moves on rollers recessed in the
chassis rail.
Pointing in azimuth is performed by an endless chain
engaging in a sprocket* bed around the platform. The chain
passes over a windlass, W, which is rotated by the crank, K,
The loading scoop, s, is on a lever, L, which is rotated by
a geared crank so as to bring both the charge and the pro-
jectile into the position of loading.
In order to minimize the number of men required for
loading, the act of lowering the scoop stores up energy in
certain springs so that the maximum pressure which can be
counted on shall be continuously apphed, as in the hydraulic
buffer.
The steel shield, /, protects the gunners from light pro-
jectiles.
Advantages, The carriage is low, stable, and as seen in
figure 9, very compact. The use of rollers increases its
mobility and their number distributes the thrust over a large
area. All wheels are protected and the traversing chain is of
* See Webster.
XXIII. — VARIOUS ARTILLERY CARRIAGES. 7
rustic simplicity and easy of repair, even in action. The
arrangement of the scoop facilitates loading since its load
may be placed by simply tilting the hand truck on which it
is brought from the magazine.
Sea Coast Mortar Carriages. Figures 10, 11.
Although of an entirely novel design, the carriage in figure
10 resembles essentially the gun carriage just described. The
nomenclature is the same in both figures.
The chassis is divided into two portions, Ci, C^ ; the sur-
face of contact being cylindrical about the axis of the trun-
nions. By this arrangement fon all angles of fire the axis of
the gun is always in the plane of the axes of the hydraulic
cylinders, so that the friction in starting is not increased by
the pressure causing recoil.
Rotation from recoil is prevented by the clips, c, c, etc.
The diminished intensity of the maximum vertical pressure
has caused this carriage to be adopted in the French Navy;
for ships now, as well as forts, are beginning to utilize the
advantages of vertical fire.
In another type of mortar carriage, shown in figure 11, also
under trial in the U. S., the chassis is made in one piece, the
direction of the recoil being downward at a constant angle of
60° This is a mean between the limiting angles of 6 for
mortar fire, viz. : 45" and 75°. The mortar is returned to
battery by springs that are compressed during the recoil.
Another form of loading scoop is also shown.
This is known as the Easton- Anderson carriage, of Eng-
lish design.
XXIV. — H0RS£ AND HARNESS.
CHAPTER XXIV.
HORSE AND HARNESS.
The horse transports his load in two ways. 1st, as a pack
horse ; 2nd, as a draught horse.
PACK HORSE.
The daily work of a pack horse is about equal to that of
five men similarly employed ; or, if he moves at a walk, he
may carry a load of 200 pounds 25 miles a day, or 5000 mile-
pounds.
If he trots, the increased expenditure of muscular energy
reduces his daily work about one-third.*
In the above the weight of the horse is neglected, and it is
assumed that, though this daily work may be temporarily ex-
ceeded, the excess cannot be long continued without injury.
The mule, owing to his build, carries more than the horse ;
he eats less and is surer of foot. He is therefore generally
used in the mountain service.
DRAUGHT HORSE.
Load.
Although a horse can pull much less than he can carry,
the advantages of the wheel enable him to draw over ordinary
roads a load weighing about seven times as much as his pack.
With a pull of 80 pounds the daily work of a draught horse
* It has been found that for any animal the maximum rate of work per
unit of time (or/ z/, Chapter XI, page 4) is attained when the velocity is
about I of the maximum velocity unloaded, and the load about g of the
maximum load at the lowest positive velocity.
XXIV. — HORSE AND HARNESS.
is generally given as 1600 pounds X 23 miles, or 36800 mile-
pounds of load, or 1840 mile-pounds of actual work.
Owing to their interference with each other's motions, the
maximum load drawn by teams of horses increases less rapidly
than does the number of horses in draught. Thus, when the
teams comprise respectively 2, 4, 6, 8 horses, the maximum
loads which they can continuously draw are in the relation
per team, of the numbers 9, 8, 7, 6.
These considerations, the mobility of the system (Chapter
XXII, page 1), the increased weight of forage and length of
column required, have generally fixed the limit of efficiency
at the six-horse team.
It is estimated that when a draught horse carries a rider,
his efficiency is diminished J at a walk and § at a trot. Con-
sequently, supplying the data given, the maximum load for a
team of 6 horses moving at a trot will be about
near files. off files.
3 X 1600 3 X 1600
+ ^
^1 = 3733 pounds;
or 622 pounds per horse.
This may be considered 2i physical constant^ the best method
of distributing which between the objects transported and the
means of transportation is still open to inquiry.
Various conditions must be allowed for : On one hand are
bad roads, insufficient food, rapid movements for short times,
and forced marches. On the other hand, the reduction in
the load caused by the expenditure of ammunition, the dis-
mounting of the cannoneers, and the infrequency of the trot.
Upon these considerations are based the following approx-
imate loads per horse.
Horse artillery, 650 pounds.
Light field artillery, 700 pounds.
Heavy field artillery, 850 pounds.
Siege artillery, 1000 pounds.
XXIV. — HORSE AND HARNESS.
REMARK.
The 12 pdr. Napoleon gun, which was the heaviest field
gun used in our civil war, and which traveled over roads quite
as bad as any used in foreign wars, gave a load of 645 pounds
per horse, and was found amply mobile. The load per horse
for the 3.2 inch B. L. R., field, is 632 pounds.
Angle of Draught.
The power of an animal in draught may be supposed to
consist in his ability to maintain himself rigidly in a position
such that the moment of his weight may be increased without
increasing the lever arm of the resistance.
Thus in figure 1, let / be the position on the ground line,
/ g, of the hind feet of the horse in draught. Let s be the
shoulder of the horse or the point at which he applies his
power to the trace, s c, which is attached to the carriage at
the point c. Let W be the weight of the horse, and / be
the distance from / on the line / s, of the vertical passing
through his center of gravity. Let r be the tension on the
trace, the length of which s c ■=. t^ and let R be the horizontal
component of r, producing uniform motion of the point c in
a horizontal plane.
Let / be the variable angle with the ground line of the line
s /, and g} be the variable angle between s f and s c. Let
^, drawn from /, perpendicular to s c, be the lever arm of
the resistance. Let the same symbols ** primed " represent a
new position of the system caused by the horse bending his
knees in pulling. For simplicity, we will suppose that his
fore feet are otf the ground and that his hind legs are not
extended so as to increase /, as these suppositions tend to
neutralize each other. Also that the center of gravity is on
the line f s.
The construction of the figure shows that, as the point s
moves to s', c will move to c\ and that R will increase until
XXIV. — HORSE AND HARNESS.
the compression along s f causes the horse to bend so that /
will shorten.
The stress R may under these circumstances be deduced as
follows :
From the equaHty of moments we have W I cos i-=.r h,
and from the figure
. W I cos i cos ii — (p)
i? = r cos (? — g)) = ^^ ^
Graphical construction shows that, as i diminishes, h and
qp will diminish slowly, and / — qp will rapidly approach zero.
R will have its maximum value when s falls on the line c p^
either from raising the point of attachment to the load at c or
from the descent of the point of appHcation of the power at s.
This value is not realized in practice, since, in addition to the
effect noted above, as i decreases the force of friction at /
decreases and the feet tend to slip.
A proper inclination of the trace is therefore valuable since
it enables R to be increased according to the ability and
willingness of the horse, and also that it enables him to draw
by increasing the friction between his feet and the ground.
By experiment it was found that when the horse is free,
the maximum practical value of R^ or about 0.6 W^ was
attained for a value of i — 9 = 12°. When the horse had
a rider, i — 9 could profitably be reduced to 7°. From
these data it is estimated that, since tan 12°= 0.2, a draught
horse should carry \ of his load on his back.
The preceding general considerations apply to the case of
men pulling on ropes or pushing on capstan bars, etc. They
partly explain also that, while for the horse the maximum
value of i?=0.6 W^ for man, it is found practic ''" that
R^W,
Arrangement of the Horses.
Owing to the difficulty of coordinating the movement of
the horses the single file is used only when the gait is slow
XXIV. — HORSE AND HARNESS.
and the road smooth, so that the shaft horse will not be un-
duly fatigued by frequent changes of direction.
When the double file is used, the control of the direction
is shared by the horses of the wheel team, provided the car-
riage have a pole.
This team is preferably attached to a movable double tree^
Chapter XXI F, page 28, since this shows by its inclination
whether the horses are pulling evenly, and also transfers the
draught to the axis of the carriage. For these reasons it is
often called the evener.
By attaching the traces to the single trees hooked on to
each end of the double tree, greater flexibiHty is attained;
and, since the shoulders of the horse are naturally brought
into bearing alternately, he is less apt to be chafed by the
sliding of the collar.
He may also, when harnessed, be more readily hitched
and unhitched.
In commerce the leading team is generally attached to
an evener fastened to the front end of the pole. This is
objectionable since it confuses the functions of the pole.
A better method, sometimes followed, is to support the
evener by the pole, and to connect it with the axle by an
independent tensile member, as by a chain.
In the present arrangement, the objections to supporting
the weight of the evener on the end of the pole, and here-
fore on the necks of the wheel team, are avoided, and the
traces of each team are connected with those in rear by an
arrangement which permits continuous draught without caus-
ing the effort of wiUing horses to be neutralized by the
laggards.
The team between the leaders and the wheelers is called
the swing team. The horse on the left of each team is
called the near horse and that on the right the off horse.
XXIV. — HORSE AND HARNESS.
Requirements,
The preceding considerations illustrate the application of
the principle of independence of function to meet the require-
ments of artillery harness which, as stated by another writer,
may be thus abridged.
" No horse should be restrained by the efforts of another,
and the direction of the traces should be most favorable for
draught. The drivers should be able to harness and unhar-
ness promptly, by night as well as by day, when benumbed
by cold and when excited by danger. The fall or loss of a
horse should not be a permanent obstacle to the advance,
and disabled horses should be easily replaced. '
U. S. Artillery Harness. Figure 2.
WHEEL HARNESS.
This is composed of four essential systems, three of which
occur in all harnesses except for horses in the lead. The
systems are :
1st. The head gear to guide and hold the horse.
2nd. The saddle to transport the driver, who, for the
independent control of his team, is mounted.
3rd. The draicght harness which enables the horse to move
the carriage forward.
4th. The breeching for moving it backward.
1. The head gear consists of the bridle and halter. To
the bit of the off horse is attached the lead rein, one end of
which is held by the driver.
2. All horses are saddled, the off horse carrying the driver's
valise, and, when necessary, an extra cannoneer.
3. The draught harness and the breeching constitute two
independent systems symmetrically arranged.
The former is composed of the following parts.
The hameSj h, figure 2, are two curved irons shaped like
the signs ( ). They are connected together below by an
XXIV. — HORSE AND HARNESS.
iron clasp, and adjusted at the top by a leather strap so as to
embrace the neck and form a rigid frame against which the
horse may thrust. To diminish the pressure per unit of area
on the horse's shoulder* the hames rest on a similarly
shaped cushion, the collar. To each hame is attached by a
flexible hinge a stout leather tug^ t. This terminates in an
iron ring through which passes the trace chain, c^ terminated
by the toggle^ t' . The latter connects the front trace chain
of the wheel horse with the rear trace chain of his leader,
and so on throughout the column. When in motion, the tug
ring plays on the trace chain and thus makes the leading
horses independent of those in rear.
The length of the rear trace chain may be varied by a
toggle to suit the conformation of the horse.
The safe, s, protects the shoulder from chafing.
The loin strap, /, sustains the trace when relaxed, and the
belly band beneath the saddle keeps it from rising over the
back in turning.
4. The breeching is composed of the broad breech strap,
b, figure 3, corresponding to the collar ; it is supported by
the hip straps h. Corresponding to the traces is a Y-shaped
system consisting : — 1st. Of the continuous breast strap, bs,
which, passing around the breast, is united at each end to the
breech strap. It is supported in front by iron Hnks hanging
from the hames. 2nd. The stem of the Y is formed by the
pole strap, p, connected at one end to the breast strap by an
iron double-loop, shaped like a figure 8, and leading obliquely
downward and inward to the end of the pole. The functions
of the pole thus correspond to those of the splinter bar
in rear.
* This end is served in modern practice by using hames of sheet steel
formed to fit the shoulder. The same principle is applied in the cavalry
saddle.
XXIV. — HORSE AND HARNESS.
Pole Yoke,
The weight of the pole is supported by the pole yoke,
which is connected by a short chain to the clasp of the
hames. The branches of the yoke are so hinged to a collar
revolving loosely around the pole that they can play only in
a plane passing through the axis of the pole.
This allows the horses to travel freely at different levels
and prevents the lateral thrashifig of the pole.
LEAD HARNESS.
The leading horses have longer traces than the wheelers
and have no breeching; otherwise their harness is identical.
Improved Harness. Figure 4.
The harness devised by Major Williston of the Artillery,
which is now undergoing trial, resembles that above described
except in the following principal points.
1st. For interchangeability, the saddles and bridles are
the same as those used by the cavalry, and saddle bags
replace the valise.
2nd. The wheel traces are attached to single trees which
may be hooked to the saddle when not in use.
3rd. The breeching is that used in commerce. The stem
of the Y passes under the horse to a transverse bar in front,
which corresponds to the evener, and is called the neck yoke.
This is the most important change from the regulation
harness. It prevents the breech strap from slipping upward
in stopping suddenly, and also avoids the oblique thrust on
the horse's neck which tends to make him fall.
The neck yoke also controls the pole better than the hinged
pole yoke.
4th. The bridle rein of the off horse passes through a
pulley on his saddle, so that, in holding him back, the
oblique stress above mentioned is further avoided.
XXIV. — HORSE AND HARNESS.
5th. The collar, instead of being continuous, is hinged
above and is provided with a fastening below in easy reach.
6th. The horse of the chief of piece is provided with a
light draught harness, consisting of a breast collar and traces,
with which in an emergency the other horses may be assisted.
When not in use the traces are folded across the horse's
withers.
This harness is distinguished for the ease with which the
horses may be detached from the carriage in all conditions of
service.
LEATHER.
That used in harness is classified according to its thickness,
into harness," bridle and collar leather.
The leather from the necks, shanks, flanks and bellies, or
the offal, figure 5, is rejected as too spongy for use, so that
only about one-half of the hide is employed. Of this, the
butt is the best portion.
The lighter hides are slit axially into sides.
XXV. — ARTILLERY MACHINES.
CHAPTER XXV.
ARTILLERY MACHINES.
Object-
Artillery machines are employed to mount and dismount
cannon and to transport artillery material from one part of a
work to another. They comprise the gin, the gun lift and
Jacks of various forms; and wheeled vehicles such as the sling
cart, the truck, etc.
Machines Used in Mounting Cannon.
The gin consists of a tripod composed of two legs which
form a shear or derrick, and a pry pole by which the legs
are lifted and braced.
The hoisting apparatus consists of a block and fall sus-
pended from the apex and operated by a windlass supported
by the legs in a position convenient for the use of handspikes.
The use of the gin is confined to relatively light weights.
Heavy weights are preferably lifted by the hydraulic jack and
loose blocking.
The hydraulic jack is a compact form of the hydraulic
press, which contains within itself the reservoir of liquid
required. It is provided with valves by which the direction
of the motion of the ram may be varied.
Other jacks apply the principles of the lever and the screw,
and are correspondingly named.
The gun lift consists of two massive trestles so framed that
they may be easily dismounted for transportation.
Each trestle carries on its beam a hydraulic jack ; the latter
by means of a lever raises a bar of iron which passes verti-
cally through the beam and the lever, between the jack and
the fulcrum of the lever. This bar is pierced at short inter-
vals by holes, and its lower end is formed into a hook.
XXV. — ARTILLERY MACHINES.
Both bars having been attached to the weight, and a pin
having been passed through the hole in the bar next above
the lever, the ram of the jack is raised to its full extent. A
pin is then inserted through the hole next above the beam
and the ram is lowered. The upper pin is then shifted down-
ward and the operation continued.
For comparatively light weights a single trestle may be
employed like a gin.
Machines Used in Transportation.
Heavy weights are usually transported by the aid of cap-
stans and rollers.
When space permits, cannon may be rolled bodily by par-
buckling. In such cases a muzzle collar of the maximum
diameter of the piece corrects the circular path which the
conical mass tends to describe.
Heavy weights may also be rolled through the narrow
passages of forts on a low framework called the cradle.
The wheels of sling carts are large and have but little dish.
Since, hke the gin, they suspend the load, they are relatively
weak, and hence are used for lighter weights than the cradle.
By mechanical appliances mounted on the axle, the weight
may be lifted from the ground, and during transportation
may be permanently secured to the axle by hooks which
relieve the more delicate mechanism from shocks.
The means of lifting are the screw, and the hydraulic jack
which works on the principle explained for the gun lift.
For light weights the eccentric position of the hooks may
enable the weight to be raised by lifting the pole before the
weight is attached and afterwards by depressing it. This
means of lifting is applied to the iron sling cart. The field
limber may be similarly used to carry a piece, the carriage of
which is disabled.
In transportation the pole of the sling cart is supported by
the limber.
XXVI. — HAND ARMS.
CHAPTER XXVI.
HAND ARMS.
The weapons carried by the soldier, or portable arms may
be divided into hand arms and small arms.
The former class is known in French as '^armes blanches ; "
the latter requires, as in cannon, a preliminary study of the
ammunition employed. See Chapter XXVII.
Classification.
Hand arms are divided into
1st. Thrusting arms which act by the point.
2nd. Cutting arms which act by the edge.
These functions may be combined in the same weapon,
though at some sacrifice of efficiency.
Thrusting Arms.
The body of a thrusting weapon should be straight so as
to avoid a rotary moment on impact, and the center of gravity
should be placed near the handle. This may be attained by
fluting the blade, or by suitably weighting the handle.
The principal thru^sting weapons are the straight sword, the
lance and the bayonet.
The sword is composed of the blade, the hilt by which it
is held, and the guard. A knob sometimes acts to counter-
poise the blade as in the foil.
The lance is composed of a short steel blade fixed to the
end of a wooden handle about 10 to 16 feet in length. The
handle is furnished with a leather arm-loop placed over the
center of gravity.
XXVI. — HAND ARMS.
After a long period of comparative disuse, in spite of the
greatly increased efficiency of small arms, its use abroad is
now becoming more general. In this country it has never
been successfully employed.
The bayonet is useful principally for guard duty and for
its moral effect. Like other hand arms, it has the merit of
"never missing fire."
The objections attending its weight and that of its scab-
bard, and its eccentric position in firing may be partly over-
come by combining its functions with those of the ramrod.
Attempts have also been made to turn it into an intrenching
trowel. The tendency is now to shorten it to the proportions
of a dirk, which may form a useful knife.
Cutting Arms.
The efficiency of these arms is promoted by increasing the
distance of the center of gravity from the handle, and by giv-
ing a curvature to the cutting edge so as to develop on impact
a tangential or slicing component which will call into play
the serrated edge possessed by even the sharpest knife. This
enables the weapon to rupture in detail the muscular fibers
on which it acts.
Description.
The principal cutting weapon is the saber. Sabers are
classified according to their use. In the U. S. service there
are two kinds, viz. : the cavalry saber and that for the light
artillery.
The cavalry saber, being used on horseback for thrusting as
well as for cutting, has but a slight curvature, a long blade,
and a basket hilt (properly a guard) which carries the center
of gravity toward the handle.
The light artillery saber being intended for hand to hand
conflict by troops, who for the service of their batteries are
XXVI. — HAND ARMS.
dismounted, is shorter than the cavalry saber, is more curved,
and has a guard composed of a single scroll of brass.
Remarks.
The present tendency is to make the artilleryman depend
for his personal defence upon the gun which his duty to the
other troops compels him to serve to the very last extremity.
He should therefore be free from any incumbrance which
will distract him from his proper functions.
In order to avoid the exposure of the person in cutting,
many cavalry officers are in favor of avoiding the objections
to the combined functions of the cavalry saber by using it
solely for thrusting.
On the other hand the swordsmen of East India, than
whom there are few more expert, prefer blades which are
greariy curved, the radius of curvature of some being about
18 inches.
The following discussion illustrates the effect of curvature,
frequently utilized in the useful arts.
^ "-V s' ^'"'
Let O S Ph^ the edge of a curved blade rotated around
O and striking at P with a blow, P F, at right angles to
OP, ThenP T=PPcQS(p =PF cos i^ Z' r is the tan-
gential component, and this will be measured by P P cos
C P Oj which gives an easy method of discussing the effect
of curvature. If, as in the artillery saber, S', the radius of
XXVI. — HAND ARMS.
curvature, be shortened by placing the center at C ; or, if
as in some Eastern blades which have a tangential handle and
also in the common scythe, the center of rotation be placed
above the line P O, the value of cos (p will be increased and
so will the proportionate value of the tangential component.
On the other hand if, as in the cavalry saber, the handle
be lowered as to O, in order to increase the tangential com-
ponent in thrusting, the slicing component will decrease.
XXVII. — SMALL ARM AMMUNITION.
CHAPTER XXVII.
SMALL ARM AMMUNITION.
The Eelation between Arms and Ammunition.
As seen in Chapter V, the efficiency of all fire arms has
been dependent principally upon the nature of their ammu-
nition.
This may be called the food of the gun as the means of
conveying it to the chamber is actually called the feed. As
a rule the gun must be made to fit the ammunition as a shoe
should be made to fit the foot.
MUZZLE LOADING AMMUNITION.
Powder and ball were originally carried loose; but for
some time the greater rapidity of fire with arrows at the
ranges common to both weapons, caused the latter to be
preferred.
Gustavus Adolphus made important improvements in the
ammunition.
He first provided separate receptacles for each powder
charge ; these were called cartridges from their paper
envelopes. (Latin charfa, paper.)
He subsequently combined the powder with the projectile
in the paper wrapper, which, until about 1865, formed the
principal ammunition for small arms. See Figure 1.
In addition to the comparative disadvantages of muzzle
loading arms cited in Chapter XI, may be named the vari-
able amount and condition of the powder in the chamber,
since the powder was but imperfectly protected from moist-
ure and was hable to be wasted in loadmg. There was also
XXVII. — SMALL ARM AMMUNITION.
the danger of inadvertently loading tlie piece with more
than one cartridge at a time. Nearly one-half of the
muskets abandoned at the battle of Gettysburg were found
to contain more than one cartridge.
In spite of the theories of those who feared that increased
rapidity of fire would lead to a disastrous expenditure of
ammunition, there has always been the feeling expressed by
Frederick the Great in saying, that other things being equal,
" He who fires fastest hits most."
BREECH LOADING AMMUNITION.
Non-metallic Ammunition.
The state of the arts required the first breech loading
ammunition to be formed after the manner of that just
described ; and, as it was impossible to permanently prevent
the escape of gas by the close fitting of the parts of the
breech, the joint required for rapid loading was generally
placed in front of the chamber, from which position the
soldier would suffer least from the discharge.
To facilitate loading the section of the barrel containing
the chamber was caused to oscillate about an axis in rear;
so that, the paper cartridge having been broken for loading,
the bullet acted as a stopper to prevent the exposure of the
loose powder before the piece was closed.
This structure distinguishes a large class of arms, now
obsolete, which are known as having 7novable chambers.
This includes the Hall rifle, used in this country in the early
part of the century. It is believed to be the first breech
loading small arm used by troops.
The operation of such guns was necessarily slow and
defective.
METALLIC AMMUNITION.
Origin.
The primed metallic cartridge case, invented in France,
was first used by troops during our Civil War. It contained
XXVlt. — SMALL ARM AMMUNITION.
all the components of the ammunition, under invariable con-
ditions, in an envelope which formed a gas check, and was
therefore adapted to arms in which the chamber was fixed.
Being rigid and of exact dimensions it could be and was
at first most extensively used in magazine arms, in which
the operations of loading are automatically performed.
Rim Fire.
In order to support it against the blow which exploded the
fulminating priming, and to extract the empty case, it was
provided with a rim. For simplicity of manufacture, and
because the arms in which it was principally employed con-
tained the cartridges in tubular magazines and were carried
by mounted troops, the fulminate,/, was placed within the rim,
as shown in figure 2.
This construction, although confusing the functions of the
rim and the primer, was intended to prevent accidental ex-
plosions in the magazine.
For the small charges of powder then used, the metal could
be made thin enough for certainty of fire, since it was com-
posed of soft copper.
Figure 2 shows that such a cartridge, having what is termed
a folded head, is necessarily unsupported by the walls of the
chamber for a length at least equal to the thickness of the
metal forming the rim. Consequently, as charges and pres-
sures were increased, the rim fire cartridges were found to
shear across the edge of the chamber ; and the copper was so
deficient in elasticity that they would resist extraction.
The quantity of fulminate contained in the rim was much
greater than was required for ignition at any one point, and
further tended to destroy the fold. The distribution was im-
perfect and misfires were frequent.
The cartridge could not be reloaded.
XXVII. — SMALL ARM AMMUNITION.
Central Fire.
As metallic ammunition became more generally employed
in all arms, these objections led to the use of the center fire
cartridge, now universally employed ; these objections led
also for a time to the disuse of magazine arms.
The adoption of central fire permits the case to be strength-
ened indefinitely in the shearing plane ^ and to be made of
an elastic material like brass, the special elasticity of which,
developed by its manufacture, facilitates its extraction. It
also permits the reloading required by the great expenditure
of ammunition m target practice.
Folded Head.
The first center fire cartridges were made with folded heads,
as the arts then furnished no other method of forming the rim.
To avoid shearing, a thin, cup-shaped, gas check, as shown in
figure 3, was, and is still employed. This contains a central
hole to allow the flame from the fulminate, /, to pass through
the vents, vv^ in the anvil, a.
The Ordnance Department for several years made the copper
cup-anvil cartridge shown in figure 4. In this it was attempt-
ed to combine in one piece the functions of the gas check
and of the anvil. But these were inconsistent, and the cart-
ridge, although avoiding objections urged against a per-
forated head which contained a loose primer, was abandoned.
The limit of resistance to shearing was soon reached,
because, owing to the manufacture, the maximum thickness of
metal is that of the head. So that if a thicker or more elastic
metal was used misfires would result, unless the energy of the
blow required for ignition was so much increased that the
rapidity of fire was diminished.
The flat anvil, figure 5, demanded by the obhque firing
pin of the Springfield rifle, requires a more powerful blov/
than does that shown in figure 3, and the thickness of metal
XXVII. SMALL ARM AMMUNITION.
requires the firing pin to be sharp. On the other hand, the
anvil of figure 3 is well adapted to the axial blow of a flat
pointed pin. This requires less work in cocking and is less
apt to pierce the cap.
Solid Heads.
The state of the arts now permits the U. S. cartridge to be
made with a solid head, as in figure 5. The shearing plane
lies in front of the edge of the chamber even when, owing to
the yielding of its support, the case may be forced backward
in firing.
Certainty of ignition now requires that the anvil shall be
renewed at every fire. Consequently the primer is assembled
before issue with its anvil and fulminate complete. The
resulting variation in figure 3 is shown in figure 6.
An objection to the solid head cartridge arises from its un-
equal expansion when fired. The mouth, being thin, is more
firmly held by friction against the walls of the chamber than
is the thicker portion in rear, so that the latter may slide
backward to the extent permitted by its support. Cases
which have been often reloaded are found to tear across by
longitudinal stress.
The Morse cartridge, figure 7, provides for this by making
the head entirely separate from the body of the case.
Remark,
The influence of improvements in metallic ammunition has
probably reached its limit in the cartridge employed in rapid
firing cannon, Chapter XXIX, page 18. The size of the
cartridges which these employ is limited by the weight which
one man can conveniently handle.
METALS USED FOR CARTRIDGE CASES.
Copper was first employed on account of the ease with
which it could be worked. When alloyed with a small pro-
XXVn. — SMALL ARM AMMUNITION.
portion of zinc it was until recently preferred by the U. S. to
brass, which, when in contact with gun powder, undergoes in
time a molecular change that renders it as brittle as baked
clay. It is said that the discovery of this defect in the
Russian ammunition postponed the war of 1877.
The deficient elasticity of copper accounts for the preva-
lence of the lever used for extraction in early breech loading
arms, and for their comparative slowness of fire.
Brass is cheap and so elastic that guns in which it is used
may be opened by the direct action of an axial bolt. For
the reasons given, Chapter XXVIII, page 6, the rapidity of
fire of such arms is increased. This is the metal now
generally employed. In order to protect it from the powder
the cavity may be varnished or tinned.
The elasticity of brass adapts it to reloading since resizing
is less necessary than with copper.
The operation of resizing is required by unavoidable dif-
ferences in the chambers of different guns. The brass cart-
ridges used in the rifle, Cal. 0.45 may often be reloaded for
use in the same gun without resizing them ; but owing to the
greater pressures found in the new Cal. 0.30 rifle, firing smoke-
less powder, resizing is always required for this arm. See
Chapter XXVIII, page 3.
Low steely when protected from oxidation, is proposed as a
cartridge metal, on account of its strength elasticity and
freedom from structural change.
MANUFACTURE OF METALLIC AMMUNITION.
The cartridge case may be made in two general ways,
viz. : 1st, by coiling by hand a thin sheet of metal into a
tube ; 2nd, by drawing the tube from a thicker disc as de-
scribed in Chapter XVIII, page 2.
XXVII.— SMALL ARM AMMUNITION.
1. Wrapped Metallic Cartridges. Chap. XVI, figure 8
The metallic sheet is trapezoidal so as to increase the
thickness of the walls near the head. This gives the ex-
terior the conical form required for extraction, while the
interior being cylindrical retains its hold on the bullet. It
also increases the thickness of the flange by which the
case is riveted to Ihe separate disc that forms the head.
This method, the origin of which is evident, avoids the
use of the expensive machinery used in the second process,
so that in an emergency the manufacture could be easily
improvised.
The cartridge is serviceable, but neither waterproof, rigid,
nor exact enough in its dimensions, for all the requirements
of service.
2. Drawn Cartridges.
The operation of drawing necessarily leaves the exterior
of the tube cylindrical, so that the required variation in
thickness is obtained by varying the diameter of the
punch.
The primary draws are facilitated by removing by an-
nealing, (/. ^., heating followed by quenching), the special
elasticity developed by the previous operations. Chapter
XV, page 22.
After having been drawn to a length slightly in excess of
that required, the tubes are trimmed to an exact length to
prepare them for the operations of heading.
The mandrel, figure 8, supports the trimmed case in a
closely fitting die. A hunter of the proper dimensions first
forms the pocket for the primer, and a second operation with
a bunter, such as shown, causes the metal to flow into the
annular space provided for the rim. The pocket is then
vented.
XXVII. — SMALL ARM AMMUNITION.
To facilitate extraction the case is tapered by forcing over
it a conical die. The cylindrical seat for the bullet is
simultaneously formed.
Components
The U, S. atwil is made from a copper wire of rectangular
cross section containing on one side a continuous groove.
From this are punched a series ot circular discs which form
the anvils, The edges of the discs are notched so as to
form a passage way for the flame of the fulminate,/, through
the notches, into the groove which bridges over the vent, z/, in
the head of the cartridge.
The bullet is composed of an alloy ot lead and tin ; the
latter metal, although it increases the difhculty of manufac-
ture, gives the hardness required to resist deformation in
the gun. Chapter XXVIII, page 3.
The bullet is made by compression between dies which
part on an axial plane. See figure 9. The cavity in the
base of the bullet may be varied to bring the bullets to an
exact weight.
The bullet is lubricated by being forced through a vege-
table wax so as to fill the cannelures, or grooves. This is
preferred to a fat, as it does not corrode the metals in store.
Common Operations
In the loading machine a measured charge of powder is
first deposited in the case and slightly compressed so as to
increase the density of loading. The bullet is next inserted
and secured by crimping the case upon it.
The finished cartridges are all inspected for weight and
dimensions.
The first is accomplished by a weighing machine which
rejects all that weigh less than a prescribed minimum. The
principal object of this operation is to detect charges in-
XXVII. — SMALL ARM AMMUNITION.
sufficient to expel a projectile which might cause a subse-
quent discharge to burst the gun.
The gauging machine makes sure that every cartridge
will enter the gun. The gauging die, which is sUghtly
smaller than the minimum chamber, verifies the length of
the cartridge to the rear from the circle of contact between
the bullet and the rifling, the profile between these planes,
and the maximun radius of the rim.
For safety the primer is sunken below the plane of the
head.
The automatic operation of the machinery has greatly
reduced the cost of manufacture, and has thus removed one
of the principal objections to metallic ammunition.
The inspection merely precedes the proof. Chapter
XVII, page 18. This consists in firing a portion of the
daily product to verify the certainty of fire, the strength of
the case, to determine the volume of the charge, the com-
pression required for the standard velocity and above all to
test the accuracy of fire.
U. S. SMALL ARM AMMUNITION.
The following varieties are now made (1891) :
1. The rifle ball cartridge, /^^q, or about 70 grains of
powder and a 500 grain bullet. / V= 1280 / s.
2. The carbine ball cartridge, /o\- ^ ^-= 1150 / s,
3. The revolver ball cartridge, f^^. I V= 730 /j-.
4. The rifle and carbine blank cartridge, filled with com-
pressed powder that is protected by a varnished paper cup,
and retained by crimping the case so as to facilitate loading.
5. The revolver blank cartridge as in 4.
Important changes in this ammunition are now pending.
Their principles will be hereafter discussed in connection
with the arm. It is significant to observe that now, as here-
tofore, the adoption of the new arm awaits the perfection of
its ammunition. Chapter XXVIII, page 19.
XXVIII. — SMALL ARMS.
CHAPTER XXVIII.
SMALL ARMS.
Classification.
Small arms may be classified according to the service in
which they are employed, as this determines the maximum
length of barrel, given to the rifle^ i\\Q carbine^ and W^q pistol.
Muzzle-loading arms, and breech-loaders having movable
chambers being now obsolete, breech-loading small arms
with fixed chambers may be classified into single loading and
magazine arms.
The latter class is now supplanting the former, because of
the moral and physical advantage of being able at will to
increase the rapidity of musketry fire.
Historical Sketch.
Some of the objections formerly made against the breech-
loader have been discussed in Chapter XXVII. To these may
be added the former fear that the mechanism might not endure
the accidents of service.
But the Prussian wars of 1864 and 1866, and the more
extended campaigns of 1870, proved that after a victory
there is generally time enough for repairs.
During the siege of Plevna in 1877, these conclusions
were emphasized by the use by the Turks, for the first time
in Europe, of the American Winchester repeater.
Although of a model now considered imperfect, its success
was conclusive.
It is now realized that the change from muzzle-loading to
breech-loading having established the advantages of rapidity,
the choice of a magazine arm is a detail to be determined by
XXVIII. — SMALL ARMS.
independent considerations. The selection is attended with
many complications which, as in the past, relate principally
to the ammunition. Some of these will be hereafter dis-
cussed in detail » but it may be premised that, while the
power ol the weapon depends principally upon the abiUty of
its (human) carriage to resist recoil ; its continued operation
depends upon the number of cartridges which this carriage
can conveniently transport.
The development is thus limited by a physical constant.
COMPONENT PARTS OF B. L. SMALL ARMS.
I. THE BARREL.
Weight.
Except for considerations relating to the recoil and the
practical necessities of service, the general use of steel would
permit the barrel to be considerably reduced in weight.
Caliber.
Although the best results follow from adapting to each arm
its own ammunition, yet in order to meet emergencies the
cartridges for the rifle and the carbine may be interchanged.
These arms are therefore of the same caliber.
For the reasons stated in Chapter XVI, since the adoption
of the rifle principle the tendency has been to reduce the
caliber. The limit is fixed by questions of internal ballistics,
and also by the nervous shock communicated to the animal
struck. Upon the shock is thought to depend the " stopping
power " of a bullet that does not kill.
Until lately the limit was generally taken at about 0.45
inch, but recent experiments have induced many countries to
reduce it still further to about 0.30 inch.
The propriety of the change is still debated, and like many
others requires the test of war. The advantage may consist
in this : that a shock which might be insufficient to stop a
XXVIII. — SMALL ARMS.
man in the heat of a close action may, at the long ranges
which the reduced caliber provides, be severe enough to cause
him to withdraw. But this would not apply to horses.
Rifling.
The cross-section of the rifling depends principally on the
nature of the bullet. If this be of a soft material, like lead,
the lands may be broad as in the Springfield rifle and con
versely, figure 15, if the metal be hard. The grooves should
be shallow and so formed as to be readily cleaned.
The increase of spherical density, which results from
reducing the diameter of a projectile of which the length,
and therefore the sectional density, is kept nearly constant,
has required a considerable increase in the twist, so that
special precautions have been required to prevent the pro-
jectile from shearing. Chapter XVI, page 10.
In the caliber 0.45 bullet this was done by alloying the lead
with tin, Chapter XXVII, page 8 ; the new bullet is more-
over coated with a thin jacket of a harder metal. Chapter
XXVII; Plates.
II. THE STOCK.
This forms the handle by which the barrel is directed. It
is made of wood on account of its lightness and strength and
its deficient conductivity of heat.
The form of the stock depends on the conformation of the
average man.
The butt is widened and curved so as to diminish the
pressure per unit of area due to the recoil. It is bent for
convenience in aiming. A rotary component of recoil is
thereby developed, which, if the crook be excessive, may
cause inconvenience to the firer.
The stock is necessarily weakened by being cut across the
grain to form a grasp, and more so by the present develop.
XXVIII. — SMALL ARMS.
ment in the volume of the parts about the breech It is
consequently frequently made in two pieces, the /// stock
being of a rigid material, such as black walnut, and the butt
itoik preferably tough, as of elm. Chapter XV, page 12.
The support m rear of the barrel should be of sufficient
area to avoid permanent deformation; and that beneath the
barrel should not be unduly rigid, since otherwise the barrel
may be distorted by the effects of moisture upon the wood.
Ill THE SIGHTS.
The position of the rear sight is determined by the limit of
distinct vision, and is so taken that the two sights and the
object shall collectively be most plainly seen.
The sights are separated as far as convenience permits, so
as to rectify their ahgnment with the object. See Chapter
XXX, page 7. They admit of a permanent correction for
jump and a variable correction for range, drift and the effects
of wind.
The increasing flatness of the trajectory and the growing
rapidity of fire will, except for sharpshooters, probably
diminish the number of adjustments now given to the rear
sight.
It is probable also, that instead of providing an extension
to the slide for use at extreme ranges, a separate pair of sights
will be placed on the side of the arm. The ordinary func-
tions of the members of this pair will be reversed; that is, the
rear sight will be fixed and the front sight movable down-
ward, so that a considerable elevation may be attained with-
out great variation in the relative positions of the eye of the
marksman and the point of his body which receives the recoil.
It may be remarked that the requirements of sights for war
service and for target practice at kiiowti distafices are in many
essentials incompatible.
XXVIII. — SMALL ARMS.
[V. THE MOUNTINGS.
The bands, screws, pins, etc., are intended to connect the
parts ; and the butt plate, tip and the extension of the guard
beneath the small of the stock are intended to protect from
wear and to strengthen the relatively perishable wood.
Functions.
V. THE BREECH MECHANISM.
The functions of the breech mechanism are five, viz. : to
open, load and lock the breech, to fire the charge, and to
remove the empty shell.
The manner in which these functions are performed
depends primarily upon the manner of opening and closing
the breech, as is shown by the following scheme :
Classification of B. L. Small Arms.*
o 2
a> ?
u ^
■5 «
as
Barrel,
which
slides
b
...2.
...3.
Breech
block
which
rotates
about J JUo axis of gnn.
an axis 1 Lto axis of gun.
which is [
slides I Jltoaxis of gun 4.
^^'"^^ 1 Lto axis of gun 5.
f 1 1 to axis of gun 6.
fin front of block 7.
L to axis .
of gun. 1
not in front of 1
block. I
No. Examples.
(Rare).
Revolvers t
Shot guns.
Bolt guns.
Sharps, (Krupp).
Joslyn, Warner.
( Springfield,
I Remington.
Martini.
, movable chambers (obsolete) 9. Hall, Burnside.
Discussion of Table.
The mass of the barrel renders the classes, 1, 2, 3, unsuit-
able for the military service except when, as in revolvers, the
mass is greatly reduced.
* For a fuller discussion, see Report Chief of Ordnance, 1873.
t The classification ot these is difficult. For some reasons they may
be considered as movable chambers, and in other respects they may be
considered as an aggregation of barrels of reduced length.
XXVIII. — SMALL ARMS.
Classes 5, 6, 8, are objectionable, as their operation does
not assist in loading the cartridge, but rather, as the French
say, to guillotine it.
They possess, however, the advantage of naturally resisting
the pressure which tends to blow open the breech or to
" unlock'' it.
Class 7 naturally forms a lever, formerly useful in forcing
into the chamber a deformed cartridge or in extracting one
that stuck. Arms of classes 4, 5 and 8 were frequently pro-
vided with levers.
Bolt System.
But, as the quality of the ammunition has improved, the
arms of class 4 7vithout levers^ have grown mto general use.
The following are the principal objections which have
hitherto prevented the more general adoption of the bolt gun,
although its advantages were recognized by the Prussians as
early as 1847.
1. The risk of premature discharge from striking an over-
sensitive cartridge in loading.
This was long considered an insuperable objection, but, as
will be seen, has been overcome by very simple means.
2. The danger resulting from the necessity of loading the
piece at a full cock.
This objection neglected the supreme advantage of the
rapidity of fire which results from suppressing a discontinuous
motion,* and which is further increased by the facihty with
which the reciprocating motion of the bolt adapts itself to
the demands of magazine arms.
To illustrate the latest type of this arm, the American
Lee system is described, as it contains in probably the best
*The word is used as in the drill book.
XXVIII. — SMALL ARMS.
and simplest form the elements of the mechanism required
for performing the functions above named.*
Lee System (as single loader) Figures 1 and 2.
Descripiion,
The receiver, of approximately cylindrical form, is screwed
to the breech and receives the mechanism. It is bored out
and slotted to permit the axial motion of the bolt. The slot is
widened to the front to form the well of the receiver, through
which the operations of loading and ejection are performed.
The rectangular shoulder at a forms a support for the locking
mass, a\ of the bolt in firing, and the oblique edge at b gives a
short, spiral motion to the bolt as the locking mass is ap-
proaching or leaving its support.
The system is mortised vertically through the well to receive
the magazine. As this is a special feature of the arm, its
consideration is deferred until the features common to the
best bolt guns have been discussed.
The reciprocating motion of the bolt sets the whole
mechanism in motion.
The /ia7idle is placed in rear and is curved downward so
that the hand need not leave it in firing.
A lug diametrically opposite to the locking mass engages
with a corresponding recess in the bore of the receiver, so
*The Prussian Needle Gun used a combustible cartridge case, the
fouling from which tended to obstruct the chamber ; the joint was most
imperfectly sealed, the flames escaping not only around the end of the
bolt, but into the channel traversed by the firing needle. The tactical ad-
vantages of the arm, however, offset these very serious objections, so
that it was retained unchanged until adapted to metallic ammunition
after the war of 1870.
Its opponent in this war, the Chassepot, was of similar construction,
but possessed for the end of the bolt a gas check, from which that of
Colonel De Bange is derived.
XXVIII. — SMALL ARMS.
that, by making the support symmetrical, certain objectionable
vibrations of the barrel may be avoided.
The bolt contains an axial firing pin which is surrounded
by a spiral main spring and secured to the hammer.
The bolt carries in front and to the right a hook shaped
extractor^ which, like the hammer, is so disposed as to share
only in the motion of translation which the bolt receives.
The extractor is retained by a flat spring which serves also to
key the system together.
Operation.
To open the piece, raise the handle so that the locking
mass may lie in the prolongation of the slot, and withdraw
the bolt.
The incipient rotation of the bolt is ingeniously commuted
into one of translation at each of its ends ; as follows : —
In rear, a radial projection on the bolt strikes an oblique
surface on the hammer and forces it back relatively to the
bolt until the point of the firing pin is retracted, or withdrawn
behind the plane surface in contact with the cartridge. To
avoid premature explosion the point of the firing pin is kept
back until the desired moment of discharge.
In front, the spiral motion due to the surface, b, forces the
bolt slowly back from the barrel so that power is obtained to
start the fired cartridge case from its seat. This slow and
therefore powerful motion of extractiofi is commonly used.
A rapid motion might cut through the cartridge rim and dis-
able the rifle.
As the bolt is withdrawn, the extracted case foflows until it
passes from the chamber. The rim then strikes the ejector
stud, a projection on the bore of the receiver opposite to the
path of the extractor. The case is thereby rapidly revolved
about the hook and ejected, or thrown clear of the gun.
A cartridge may then be dropped into the well, the bottom
XXVltl. — SMALL ARMS.
of which is nearly continuous with the lower element of the
chamber. A reversal of the motions forces the cartridge into
,<lace and locks the breech.
The surface, ^, now serves to prevent the shock referred to
on page 6, and also to make the motion of the hand con-
tinuous.
In the final motion of closing, the mainspring is fully com
pressed, or the piece is cocked, by the interposition of the
sear, the nose of which arrests the forward motion of the
hammer while the bolt moves on.
The U shaped sear spring acts against the trigger through
the sear; so, that when the trigger is drawn, the sear spring
is compressed, the sear is lowered -and the hammer allowed
to fall.
Remarks.
Opening^ closing and loading. These operations are safely
and rapidly performed.
Locking, The method is of great simplicity and affords a
sohd support. Jointed surfaces, however well made, permit
an objectionable displacement under the stress of firing.
Firing. The coiled spring is admirably adapted to the
purpose, since, owing to its developed length, the stress on
any of its spires is slight ; and, owing to its position on the
pin, it will continue to work, even if broken.
Extraction and ejection. These are readily performed,
Vven with inferior ammunition.
Assembling. The parts are few in number, strong and simple.
They are arranged so as to avoid the effects of rust and dust,
and are so connected as to be readily dismounted for cleaning
without the use of special tools.
MAGAZINE ARMS.
If by any means a succession of cartridges can be auto-
matically placed in front of the bolt as it is closing, a mag-
azine gun will result.
10 JCXVIIl.— SMALt ARM§
This has been accomplished in many ways which may be
classified. 1st. According as the niagazmes are tubular, or
box shaped, 2nd. According as they are permanently fixed
to the gun, or are detachable. The tubular magazines are
always fixed.
TUBULAR MAGAZINES.
These may lie either, 1st, in front, as beneath the barrel,
or 2nd, in the cylindrical volume lorming the small of the
stock and its prolongation in rear.
A spiral spring forces the contents of the tube toward the
receiver, and a valve regulates their entrance.
In the first class a carrier, operated by the withdrawal of
the bolt, raises the cartridges successively from the mouth of
the tube to the mouth of the chamber. See figure 3 for one
form of carrier.
The operation is that of the bell crank. Chapter XXIX,
figure 7^
Advantages.
This form of magazine, used in the French Lebel Rifle,
adapts itself to the profile of the gun. When in front, the
capacity is large for cartridges which are short and thick, and
a simple trap door on the side permits the magazine to be
filled without opening the breech, /. e., luithout unloading the
gun.
Disadvafitages.
The cartridges lie end to end, and in firing are exposed to
shocks which may explode them or deform them sufficiently
to interfere with the regularity of the feed.
The feed acts in the direction of the longest dimension of
the cartridge.
For the front magazine the weight is not well distributed ;
and for that in the butt the capacity is smal^, and the filling
XXVIII. — SMALL ARMS. 11
of the magazine is complicated with the unloading of the
gun.
The operation of filling is slow, since the cartridges are
passed in singly ; and, since nothing external indicates the
state of the supply, the control of the fire by the soldier, and
of the soldier by the ofticer is impaired.
The "Cut-off."
By a device which may limit the withdrawal of the bolt,
the magazine may be 'Wut-ojf and its contents reserved for
a suitable necessity. The piece meanwhile is used as a single
louder.
Such attachments are fragile and in moments of excitement
are confusing. When tried under such circumstances, they
have been found unsuited to the conditions of service.
BOX MAGAZINES.
By placing the cartridges side by side in a box, many of
the objections urged against the tube disappear. The
principal point to be decided relates to whether the box
shall be detachable or fix
1. Detachable Box-
An example of this type is seen in the Lee magazine,
figure 2, which consists of a box of sheet steel, in which the
cartridges lie over the feed spring, N.
The box is readily inserted through the mortise in the well
of the receiver into the position shown.
The operation of the bolt passes the cartridges in succes-
sion into the chamber, and acts as a valve to regulate the
ascent of those lemainmg to be fired.
A number of these magazines are carried by the soldier,
who IS expected to use his arm as a single loader until he
receives the order to fix magazines.
12 XXVIII. SMALL ARMS.
This facilitates control by the officer, but the uncertainty
of the soldier as to the state of the supply may lead him to
go through the motions of firing with an empty arm.
The principal objection to the system applies to the ex-
cessive weight and cost of the box as a package, if many
magazines are carried; and, if but few, to the probabiHty of
losing so important a component in the act of replacing it
under fire.
2. Fixed Box.
I. A prominent arm of this type is the Austrian Mannlicher
rifle, figure 4.
The cartridges are held by their bases in a sheet metal
frame, the whole package being bodily inserted into the
magazine through the well of the receiver, where it is retained
by a spring latch, r, A follower^ /, impelled by a strong
spring, ^, lifts the column so that the top cartridges are suc-
cessively shoved into the chamber by the bolt. The fall of
the empty case through the bottom of the magazine warns
the soldier that the magazine is exhausted.
In a recent model the heads of the cartridges are so held
by the frame that they lie in the same plane. With this
model no special care is needed in inserting the frame into
the magazine; while in that shown, the obliquity of the frame,
caused by the step-like arrangement of the heads, may cause
confusion.
The device for locking the arm consists of a brace, b^
attached to the bolt. It is forced downward in front of a
shoulder, t", in the receiver, by a wedge-shaped projection
below an axial stem to which the knob, k^ is attached. By
simply pulling on the knob, the brace is lifted from its seat
by the wedge, and the brace, knob and bolt slide out together.
This arrangement avoids the rotation of the bolt required
in the Lee and in almost every other bolt gun.
XXVIII. — SMALL ARMS. 13
This arm cannot be used as a single loader.
2\ The Schulhojf magazine rifle, figure 5, may be used as
such or as a single loader.
The cartridges are carried in an annular box, beneath the
receiver.
The axial shaft, s, carries a radial plate, ox follower, f, that
ia turned m one direction by the act of opening the lid, /,
figure 6, and m the other direction by a spiral spring (not
shown) surrounding the shatt, which is twisted in the act of
opening.
The cartridges may be thrown in loosely, or may be loaded
in mass from the quick loader shown in figure 7.
A circumferential slide, <:, operated by the thumb piece /,
forms a very simple cut-off.
The strength and solidity of the magazine enables it to be
slit, so that the state of the supply may be seen at a glance.
The position of the box enables it to be filled without
unloading the arm.
Quick Loader.
A cheap quick loader, figure 7, containing the supply of
cartridges for one magazine enables them to be transferred
to it in mass when rapid recharging is required. For this
purpose the lower end of the quick loader being placed over
the mouth of the magazine the pressure of the thumb of the
operator on top of the column of cartridges forces them
down into the magazine against the resistance of the
magazine spring.
They are retained by a valve at the mouth of the magazine,
and the quick loader is then thrown away. The valve serves
to retain successive cartridges singly loaded.
Form Proposed.
The eventual preference of the fixed or the detachable
box magazine will probably be largely determined by moral
considerations.
14 I XXVIII. SMALL ARMS.
The dispersed formations of future wars will probably
require a more extended exercise of discretion in the lower
grades than has hitherto been customary. The question
arises, how far down will the discretionary control of fire
extend ?
It is now proposed to attach the box magazine perma-
nently to the receiver, and ordinarily to load the arm con-
tinuously through the magazine, so that the cartridge last
inserted shall be the first to be fired and that the number
remaining shall be automatically held in reserve.
It is possible that the time gained by making the opera-
tion of the piece simple and invariable, as in the type pro-
posed, may be so utilized in the general instruction of the
troops that it will not be considered necessary to burden
them with an inferior weapon in order to control their fire.
REQUISITES OF A MAGAZINE ARM.
The preceding considerations enable us to name the fol-
lowing necessities :
1. The best ballistic conditions attainable. These may
modify the size and proportions of the cartridges, and so
affect the capacity of the magazine.
2. Consecutive rapidity of fire as a single loader as great
as that of any other arm, and the greatest possible inter-
mittent rapidity when the magazine is employed.
3. The possibility of filling the magazine with single car-
tridges, or " in mass," without unloading the piece.
4. A maximum capacity which is yet to be determined
by experience. It will probably be about 5 shots in the
magazine.
5. A ready view of the state of the supply.
6. The most simple construction compatible with the
maximum efficiency under the conditions of service.
Beyond a certain point objections to complexity become
Xxviii. — Small arms. 18
pedantic, since experience shows that the instinct of self-
preservation may be counted on for the care necessary to
maintain an efficient arm.
THE SPRINGFIELD RIFLE.
History.
This arm, although originally intended as a means of
utilizing the large supply of muzzle loading muskets left by
the Civil War, has acquired a standing which, in 1886,
caused its preference by 73 per cent of the officers to whom
were submitted, for comparative trial in service, three of the
best magazine arms.
Apart from the excellence of its manufacture and the ease
with which it may be operated with but one hand, this pre-
ference may be attributed to the independent action of a
form of lock, the outgrowth of centuries of experience ; and
the perfection of the apparatus for extraction and ejection.
The design of the cam latch and of the firing pin are
exposed to criticism.
As a reserve supply of this arm is likely to be retained for
many years after the adoption of a magazine gun, a few of
its principles are described. The nomenclature is supposed
to be known.
Operation. Figure 8.
Locking.
When the piece is fired the tendency of the block to swing
upward out of the receiver, A^ is corrected by the loose fit
of the hinge pin, E^ in its hole. The block, therefore, sHdes
bodily to the~rear until stopped by the interposition of the
body of the cam latch F, between the block and the breech
screw, C. The journals of the cam latch are loose in their
bearings so that they may be free from strain.
The centre of pressure on the breech screw is brought
16 XXVIII. — SMALL ARMS.
as nearly as possible in the prolongation of the axis of
the bore so as to diminish the tangential component of the
pressure, which tends to revolve the cam latch and tlirow
open the block. This is imperfectly resisted by the friction
developed by the normal pressure between the surfaces in
contact, and also by the combined action of the thumb piece
and the hammer, the functions of which are thereby perverted.
Extraction.
The power needed for extraction results from the compound
lever formed by the breech block and the extractor, J,
Ejection.
In opening the block the revolution of the extractor com-
presses the coiled ejector spring, K, until the action line of
this spring passes from above the axis of rotation to below it.
The expansion of the spring then rapidly revolves the ex-
tractor. This impels the cartridge case against the ejector
stud Z, which deflects it upward and throws it clear of the gun.
Firing Mechanism.
The lock, figures 9, 10, 11, consists of the lock plate, to
which the parts are attached and by which the mechanism is
secured to the stock by the side screws.
The hammer, A^ outside the lock plate, and the tumbler, B^
inside of it form mechanically but one piece, the arrangement
adopted being required for the protection of mechanism from
dirt.
The tumbler, B, is connected with the mainspring by a
swivel, y, so disposed that the resistance to cocking the piece
shall be nearly constant. This is accomplished by the varia-
tion in the lever arm of the mainspring ; as the resistance of
the mainspring due to its compression increases, the action
line of the resistance passes nearer to the axis of the tumbler,
kXVlIt. — SMALL ARMS. 17
while the lever arm of the power, the thumb, is constant.
The tumbler is thrice notched to receive the nose of the sear,
E. This, under the action of the sear spring, G^ maintains
the hammer at the distances from the head of the firing pin
required for convenience of transportation, safety of loading,
and certainty of fire, respectively.
The bridle, C, holds the parts together.
The oblique blow of the firing pin is objectionable. Chap-
ter XXVII, page 5.
RECENT DEVELOPMENT OF SMALL ARMS.
PHYSICAL CONSTANTS.
Owing to the mechanical improvements in the construction
of arms and ammunition the ballistic development of the small
arm is now limited by the soldier's endurance of its recoil.
Similarly its tactical employment is limited by his ability to
transport the burden of its ammunition ; for the maintenance
of the rapid fire of the extended lines now rendered possible
is a problem which increases in difficulty as the fire increases
in rapidity and range.
L Recoil.
These constants are influenced by racial peculiarities, and
may be considerably modified by training ; but the proper
training of large armies in the endurance of recoil implies so
great a cost, that the present tendency is to render the recoil
supportable by inexperienced troops, so that the accuracy of
their fire may not be impaired by their apprehension of its
effects.*
*Tlie effect of racial peculiarities, and incidentally of training, is shown
by the following data which relate to arms of caliber about 0.45 in.
In the relatively small armies of Great Britain and the U. S. the energy
of recoil IS about 14 ft. pounds.
The low average stature of the French fixes a limit of about 11 ft.
18 XXVIII. — SMALL ARMS.
2. Burden.
Training in weight-carrying is not expensive, and its im-
portance is becoming recognized by the frequency with which
practice marches are made. As in the artillery service
Chapter XXIV, page 2, a judicious distribution of the bur-
den between the arm and its ammunition depends greatly
upon the former's recoil.
MODIFICATIONS OF THE RECOIL.
The recoil may be reduced by modifying the arm or the
ammunition.
1. Modifications in the Arm.
If the ballistic conditions are kept constant, the weight of
the arm may be reduced, and a greater number of cartridges
be carried, by : —
, 1. The use of an elastic cushion attached either to the gun
or to the clothing.
These plans are found impracticable.
2. Increasing the mass of the gun in firing by adding to it
that of a portion of the ammunition, as in magazine guns.
The correction is variable and sometimes injurious to
accuracy.
3. Storing up the energy of recoil as by the compression of
a spring, which, by its resihence may operate the piece.
pounds. But in Germany, although the ballistic conditions are nearly
identical with the French, the desire for durability has developed the
heaviest small arm known. Notwithstanding the strength of the Ger-
mans the recoil is only 10 ft. pounds.
In Italy, as in our service during the Civil War, about 7 ft. pounds is
allowed.
This IS the limit reached by the present reduction in caliber. The re-
turn to the former standard, page 23, is significant of its practical con-
stancy.
XXVIII. — SMALL ARMS. 19
This has been tried, but so far without success, owing to the
complicated nature of the mechanism required.
4. The pressure due to the recoil may be distributed over
an increased area of the person by the proper use of the gun
sling. By lying down to fire, the path of the recoil is
shortened and the pressure on the body increased.
General consent seems to have established the weight of
the rifle at between 8.5 and 9.5 pounds.
2. Modifications in the Ammunition.
1. Caliber and Recoil Constant,
The advantages of any particular cahber being general,
that of all military rifles at any epoch is approximately con-
stant. It has recently been about 0.45 inch. See figure 12.
When the caliber and the weight of the arm are constant,
the recoil can be reduced only at the expense of the ballistic
properties of the arm. But these being maintained at the
highest value consistent with the recoil endurable in any
i 7n v V
particular case, the Equation M E ■=. C ^ - — - — - shows
that modifications in the ammunition must be confined to
factoring the momentum of the projectile. The following
considerations illustrate the effect of variations in m and z',
their product in any one case being constant.
a. If we increase w at the expense of z/, we lose in danger-
ous space at short and decisive ranges but conversely at long
distances. Chapter XX, page 40.
b. During the wars of 1870 and 1877 it was found advis-
able to deliver at extreme ranges an almost vertical fire
against masses of troops.
It has since been found that the extreme range increases
more rapidly with the sectional density of the bullet than
with its initial velocity. The present U. S. bullet was accord-
20 XXVIII. — SMALL ARMS.
ingly increased in weight from 405 to 500 grains, and an
extreme range of two miles was attained.
c. It is found that the accuracy of fire at moderate known
distances is incompatible with tlie high velocities required in
actual service. This is probably due to the vibration of the
barrel. Page 4.
Conclusion.
Owing to the impossibility of simultaneously satisfying the
requirements of the different ranges, it is considered that
efficiency at long ranges should be sought by the use of special
means, such as machine guns firing heavy projectiles. For
small arms it is considered that accuracy should become sub-
ordmate to flatness of trajectory for ranges exceeding 600
yards, at which individuals cease to be distinguished by the
unaided eye ; and that the trajectory should be so flat that
but one height of the rear sight would be required within that
distance, and the smallest number of changes beyond it.
Differences of elevation within the limits of graduation
would be adjusted by varying the coarseness of the front
sight. Chapter XXX, page 2.
2. Caliber Variable.
These conditions can be attained, and the number of cart-
ridges in a given burden increased, by reducing the caliber.
Under the conditions named on page 2, the limit of reduc-
tion has been fixed by the difficulties of manufacture and by
those relating to the cleaning of the bore.
Small Caliber Rifle.
The following general principles govern the changes in
ammunition resulting from the reduction in caliber. For
simpHcity of treatment we will first assume the muzzle velocity
unchanged from the larger caliber.
Bullet, The sectional density, and therefore the length of
XXVIII. — SMALL ARMS. 21
the bullet, has remained approximately constant ; since, as
shown in Chapter XVI, page 4, an increase in the sectional
density would increase the value of /„, unless the muzzle
velocity were reduced.
The strength of the barrel is not materially greater than
that of the caliber 0.45, and, owing to the reduction in the
area corresponding to the bottom of the bore, the increase
in the strength of the fermeture is only relative ; therefore,
the maximum value of p^ formerly allowed cannot be greatly
exceeded.
The sectional density being constant, the reduction in
caliber reduces the mass of the bullet, and therefore, although
the ballistic properties of the arm (being dependent only
upon the sectional density or C, Chapter XX, and the muzzle
velocity) would not be affected, the recoil would be reduced
(m' \ "^
— ). With the weights of bullet given in the
following table, this would reduce the recoil from about 14
foot-pounds to about 3 foot-pounds.
Powder, This reduction being excessive, the normal
endurance of the soldier against recoil is utilized by increas-
ing the weight of the charge, and therefore the muzzle
velocity.
The baUistic properties of the arm are therefore improved,
figure 12, but the internal pressure* would be excessive unless
* If in Equation (D), Chapter XII, we place K^a^ /\=z C, and repre-
IV , . w
sent by (J = -jj the sectional density of the projectile, and by « = —
the ratio between the weight of the powder and that of the projectile, we
have, after reduction.
But if, as in the case considered, 6 is constant, /„ will vary with nj^.
From this it follows that if the same charge of the same kind of powder
were used in the Hebler rifle as in the Springfield, the pressure would be
nearly doubled.
22 XXVIII. — SMALL ARMS.
the powder were made specially progressive. The value of
J for the cartridge shown in figure 14 is 11.43. See Table I,
Chapter XII.
In spite of these precautions the main difficulty in the new
small caliber high-powered guns is due to the excessive pres-
sures developed.
Powder.
The principal difficulties found in realizing the advantages
of a reduction in caliber exist in the powder.
It was thought by Professor Hebler, of Germany, to whom
much of the credit of the proposed change is due, that these
difficulties could be overcome by compressing the powder as
in a rocket, in a cartridge case like the Morse. Figs. 13, 14.
The objections to this method noted, Chapters XII, page
21 ; XVI, page 45, and the large volume of smoke resulting
from rapid fire, cause many to prefer a high explosive, such
as described, Chapter XIV, page 15 ; in spite of its recognized
objections. The complete solution of the problem is still
deferred.
Projectile,
The projectile proposed is distinguished by its penetration,
its cleanliness as regards the bore, and the nature of the
wounds which it inflicts, page 2. When they are flesh wounds
they are punctured rather than lacerated; but when they
involve the bones these are shattered.
Cartridge Case.
In order to avoid the increase in the length and weight
of the breech mechanism, resulting from the relative increase
in the length of the cartridge case, this is made bottle-shaped,
as in figure 14.
This unfits it for reloading with compressed powder, unless
the Morse cartridge be used ; the latter has been found too
delicate to endure reloading by troops.
XXVIII. — SMALL ARMS. SS
In some cases the volume of the magazine has been
diminished by eliminating the rim and replacing it by a V
shaped groove, in which the hook of the extractor may
engage, figure 16. In order to faciUtate reloading with per-
forated cyhnders of powder, previously compressed, such as
c, the cavity is cylindrical ; the reduction in diameter being
made by a brass ring, r. The blow of the hammer is sup-
ported by XhQ front of the cartridge case.
Comparison.
The following table illustrates the advantages of the
reduced cahber, since it compares the present Springfield
rifle, which is one of the best of the arms recently used,
with the Hebler, which is a fair type of the arms proposed :
Springfleld.
Hebler.
Caliber, inches
0.450
0.296
Bullet, wt. grains,
500
225
Powder, wt. grains.
70
83
Sectional density,
0.353
0.367
Spherical density.
3.6
5.6
Twist in inches,
22
4.58
Twist in calibers, ratio about,
3
1
Initial velocity, f. s.,
1280
1942
Cartridges, ratio of weights,
100
85.
Arm, weights pounds.
9.3
9.9
Maximum dangerous space, yds..
880
440
Accuracy at 440 yds., ratio
1
3
Muzzle energy, foot-pounds.
1818
1882
Recoil energy, foot-pounds.
13.95
6.11
REVOLVERS,
As a military weapon the revolver is useful principally in
enabling a horseman to use but one hand in delivering a
rapid fire. In closed masses its employment is dangerous,
24 XXVlll. — SMALL ARMS.
since it is difficult to fire to the front without striking the
horse or the leading files, and the shortness of. the piece
leads to accidents to those alongside.
It is therefore considered generally an inferior arm, and one
to be used only for personal defence and in maintaining dis-
cipline upon the field. Its ballistic properties need not be
greater than necessary to stop a man at 50 or 60 yards.
The revolver is one of the oldest forms of magazine arms.
Its present perfection is due to the invention of Col. Colt of
Hartford, who combined the cocking of the hammer with
the revolution of the cylinder.
Owing to the considerable moment of inertia of the loaded
cylinder, this tends when rapidly revolved to pass the position
in which the axis of the chamber next to be fired coincides
with that of the barrel. This is the principal difficulty found
in the construction of these arms.
To facihtate their operation, revolvers are sometimes made.
self'Cockifig, the action of the trigger causing all the motions
to be performed. For greater continuous rapidity of fire, in
which these arms, like many magazine rifles, are deficient,
the cartridges may be simultaneously extracted by sliding or
swinging the barrel and cylinder away from the breech. The
chambers may then be simultaneously reloaded by using
ammunition packed in clusters.
The complexity of these refinements and the limited scope
of the revolver generally cause simpler patterns to be pre-
ferred.
MANUPACTURE OF SMALL ARMS.
Where Made.
The service rifle and carbine are made by the Ordnance
Department at the National Armory. Pistols and such other
special arms as may from time to time be needed are bought
from private estabUshments.
XXVIII. — SMALL ARMS. 25
How Made.
Efficiency in service and ultimate economy in manufacture
require that the similar parts of arms of the same model shall
be interchangeable. This is secured by the principle of
gauging, noted in Chapters IV and XVII.
Gauging.
The general design of a gun having been perfected, an
exact working model is carefully prepared. The component
parts are so formed as to be as far as possible adapted to the
operation of the varieties of the lathe. Chapter XVII,
page 13.
Each of the components is then examined with reference
to its gauging points. These are the surfaces between which
the most exact relations are required.
For surfaces of revolution like the barrel, or parts intended
to revolve like the Springfield breech block and the tumbler,
the gauging points are established with reference to the axis
of rotation.
For pieces subject to compression, like the bolt of the Lee
rifle, the greatest pains would be taken with the distance from
the rear face of the locking mass, a', to the front face of the
bolt ; and, in the receiver, with the distance from the shoulder,
a, to the plane containing the mouth of the chamber, since
the difference of these distance must be kept invariable in
order to insure the proper working of the ammunition.
While the first of these is readily gauged, the second in-
volves the relations between the barrel and the receiver ;
each of which must be similarly watched with reference to
their abutting surfaces.
When the number of such surfaces is considerable, as in
the Springfield mechanism, the sum of their possible errors
requires the closest gauging of each link of the chain of parts.
Many forms of gauges are employed. They may be
26 XXVIII. — SMALL ARMS.
classified like patterns as positive or negative gauges, the
latter being sometimes simple notches, and sometimes mat-
rices so formed as to contain exactly pieces of an irregular
shape.
To retard their wear, the working surfaces of gauges are
made of hardened steel ; and, as steel tends in hardening
to change its form, these surfaces are finished in the hardened
state.
The number of gauges required not only for the finished
parts but for the intermediate stages demand that, before the
first arm of a series be produced, many thousand dollars shall
be expended in preparation.
When tlie gauges and the corresponding tools and fixtures
are made, the work goes on rapidly ; for the functions of each
workman are independent, and no time is wasted in fitting
the product of different hands.
In illustration: The model may cost $600 — the first hun-
dred guns made from the gauges $100 each, and the first ten
thousand, all equal in quality to the model, $15 each.
The sense of feeling is so much more acute than that of
sight, that by the use of guages differences far within the
limits of ordinary measurement may be detected. The thou-
sandth part of an inch is the customary unit, and this may
be subdivided practically according to the requirements of
the work.
The system more than anything else promotes the "division
of labor," upon which industrial prosperity depends ; and, by
substituting an absolute for a discretionary standard, it edu-
cates in a remarkable manner the workman upon whose skill
the value of the product is practically based.
OPERATIONS OF MANUFACTURE,
Barrels.
The principal operations are rolling, boring, turning,
straightening and rifling. The rolling is done as previously
XXVIII. — SMALL ARMS. 27
described, Chapter XV, page 44. While hot the rough ends
of the tube are sawed off and it is straightened under a drop
hammer, after which it is annealed by the residual heat.
When cold the hard scale is removed by pickling in diluted
acid.
In the preliminary borings the revolving auger is drawn
through the barrel instead of being pushed, so as to keep the
hole straight.* The bore is then enlarged by rapidly re-
volving reamers whose cross sections are square.
In turnhig the slide rest is guided by a template so as to
produce a conical surface, and the barrel is kept from
springing by the back rest.
Straightenifig is performed by light blows of the hand
hammer appHed at points which are indicated by the shadow
of a straight edge reflected from the walls of the bore. This
operation requires a peculiar knack which very few can
acquire.
In order to secure uniformity in the rifling^ a number of
cutters equal to that of the grooves is provided and these
are transferred automatically between adjoining grooves at
the end of each stroke of the axial rifling rod.
This rod receives a combined motion of translation and
rotation, by which, as in rifled cannon, the spiral motion is
produced.
While in an intermediate stage, the barrel is proved by fir-
ing a very large charge of both powder and lead.
The final proof of the efficiency of the mechanism and
of the accuracy of the arm is made with service ammunition.
MANUFACTURE OF THE MINOR PARTS. »
The form is defined roughly by Gorging between dies.
*The adoption of the 0.30 caliber will increase the difficulty of boring
since the barrel may require to be rolled solid and bored under
compression.
28 XXVIII. — SMALL ARMS.
The slow operation of a very powerful press permits many
parts to be reduced to nearly their finished dimensions
when cold.
The principles of milling, Chapter XVII, are used when-
ever practicable. The most complicated arms have thus
been made without requiring the use of the file.
The most interesting operations are those required to pro-
duce irregular forms.
Profiling.
The profiler is a sort of milling machine in which relative
motion in three coordinate directions can be produced between
the revolving mill and the work. To limit the relative dis-
placements the following arrangement is provided. See
figure 17.
To a table moving in a horizontal plane the work, W, is
clamped at a fixed distance from a hardened steel model, M,
of the finished part.
At the same distance from the mill, m, and with its axis
vertical, is a blank pin, /, of corresponding dimensions. We
thus have two pairs of parts ; one pair consistmg of the
model and the work and the other of the pin and the mill,
with relative motion between the pairs. When the mill begins
to cut it is necessary only to cause the pin to follow the pro-
file of the model in order to reproduce it in the work.
The intricate l^ed or matrix of the lock is thus formed with
the greatest accuracy in about one mmute.
Eccentric Turning.
This operation was devised by Thomas Blanchard, an em-
ployee of the National Armory, for the purpose of forming
the gun stock. It has been applied to many other useful
purposes, as in the manufacture of shoe lasts, spokes, and
even of statuary. Its principle is as follows: See figure 18.
In ordinary turning the cutter does not sensibly change its
XXVIII. — SMALL ARMS. 29
distance from the axis during one revolution of the work and
therefore leaves behind it a partically concentric surface.
But in eccentric turning the cutter, C, which revolves after
the manner of a mill about an independent axis parallel to that
of the work, is caused to oscillate slowly in a plane normal
to the axis of rotation during each revolution of the work, JV.
This oscillation is produced by an iron model, J/, revolving
with and parallel to the work and resting against a blank
wheel, B, attached to the oscillating frame which supports
the cutter.
In concentric turning the cutting speed is due to the tan-
gential velocity of the work, and in eccentric turning the
high speed required in wood working is due to that of the
cutter. The motion of translation is similarly performed in
both cases.
The cutting edges are placed at progressively increasing
radial distances, so as to cut to different depths during each
revolution of the cutter. This principle is frequently applied
in revolving tools.
The developed length of the cuts required to turn a gun-
stock is 13 miles ; the operation takes about 8 minutes.
Blacking and Browning.
To protect the parts from rust and to prevent them from
flashing in the sun, small pieces are blackened by heating
them until they will ignite the oil with which they are covered.
The outside of the barrel is oxidized by coating it with a
dilute acid mixture and exposing it in a warm, damp place.
The loose coating of red oxide having been brushed off, a
permanent layer of black rust remains. Some parts are
rapidly oxidized by immersing them in fused nitre.
XXIX. — CANNON WITHOUT RECOIL.
CHAPTER XXIX.
CANNON WITHOUT RECOIL.
The advantages of rapid fire from cannon would be
neutralized by the time required to readjust